## B. SIMON'S COMPLETE LIST OF PUBLICATIONS

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Citation Counts (as of 1/1/2019): MathSci Net:  18,905                    Google Scholar: 73,211 (h-index: 112)                        Research Gate: 47,949

### PAPERS

[1] Convergence of regularized, renormalized perturbation series for super-renormalizable field theories, Nuovo Cimento 59A (1969), 199-214

[2] Some pictorial compactifications of the real line, Amer. Math. Monthly 76 (1969), 536-538

[3] On the growth of the number of bound state with increase in potential strength, J. Math. Phys. 10 (1969), 1123-1126

[4] On the growth of the ground state binding energy with increase in potential strength, J. Math. Phys. 10 (1969), 1415-1421

[5] On positive eigenvalues of one-body Schrödinger operators, Commun. Pure Appl. Math. 22 (1969), 531-538

[6] (with J.J. Loeffel, A. Martin and A.S. Wightman) Padé approximants and the anharmonic oscillator, Phys. Lett. 30B (1969), 656-658

[7] Coupling constant analyticity for the anharmonic oscillator (with an appendix by A. Dicke), Ann. Phys. 58 (1970), 76-136

[8] Some comments on the Jin-Martin lower bound, Phys. Rev. D1 (1970), 1240-1241

[9] On the infinitude or finiteness of the number of bound states of an N-body quantum system, I, Helv. Phys. Acta 43 (1970), 607-630

[10] (with S. Graffi and V. Grecchi) Borel summability: Application to the anharmonic oscillator, Phys. Lett. 32B (1970), 631-634

[11] Borel summability of the ground state energy in spatially cutoff (\phi^4)_2, Phys. Rev. Lett. 25 (1970), 1583-1586

[12] Distributions and their Hermite expansions, J. Math. Phys. 12 (1970), 140-148

[13] Hamiltonians defined as quadratic forms, Commun. Math. Phys. 21 (1971), 192-210

[14] The theory of semi-analytic vectors: A new proof of a theorem of Masson and McClary, Indiana Math. J. 20 (1971), 1145-1151

[15] Wave operators for classical particle scattering, Commun. Math. Phys. 23 (1971), 37-48

[16] (with R. Hoegh-Krohn) Hypercontractive semigroups and two-dimensional self-coupled Bose fields, J. Funct. Anal. 9 (1972),121-180

[17] Determination of eigenvalues by divergent perturbation series, Adv. in Math. 7 (1971), 240-253

[18] (with L. Rosen) The (\phi^{2n})_2 field Hamiltonian for complex coupling constant, Trans. Amer. Math. Soc. 165 (1972), 365-379

[19] Convergence of time-dependent perturbation theory for autoionizing states of atoms, Phys. Lett. A36 (1971), 23-24

[20] Resonances in n-body quantum systems with dilatation analytic potentials and the foundations of time-dependent perturbation theory, Ann. of Math. 97 (1973), 247-274

[21] On the Glimm-Jaffe linear lower bound in P(\phi)_2 field theories, J. Funct. Anal. 10 (1972), 251-258

[22] A remark on groups with the fixed point property, Proc. Amer. Math. Soc. 32 (1972), 623-624

[23] Continuum embedded eigenvalues in a spatially cutoff P(\phi)_2 field theory, Proc. Amer. Math. Soc. 35 (1972), 223-226

[24] Essential self-adjointness of Schrödinger operators with positive potentials, Math. Ann. 201 (1973), 211-220

[25] Quadratic form techniques and the Balslev-Combes theorem, Commun. Math. Phys. 27 (1972), 1-9

[26] (with M. Reed) A spectral mapping theorem for tensor products of unbounded operators, Bull. Amer. Math. Soc. 78 (1972), 730-733

[27] (with F. Guerra and L. Rosen) Nelson's symmetry and the infinite volume behavior of the vacuum in P(\phi)_2, Commun. Math. Phys. 27 (1972), 10-22

[28] Summability methods, the strong asymptotic condition, and unitarity in quantum field theory, Phys. Rev. Lett. 28 (1972), 1145-1146

[29] Uniform cross norms, Pacific J. Math. 46 (1973), 555-560

[30] (with M. Reed) Tensor products of closed operators on Banach spaces, J. Funct. Anal. 13 (1973), 107-124

[31] (with F. Guerra and L. Rosen) The vacuum energy for P(\phi)_2: Infinite volume limit and coupling constant dependence, Commun. Math. Phys. 29 (1973), 233-247

[32] (with F. Guerra and L. Rosen) Statistical mechanical results in the P(\phi)_2 quantum field theory, Phys. Lett. 44B (1973), 102-104

[33] (with F. Guerra and L. Rosen) The P(\phi)_2 Euclidean quantum field theory as classical statistical mechanics, Ann. of Math. 101 (1975), 111-189
Ann. of Math.
101 (1975), 191-259

[34] (with F. Guerra and L. Rosen) Boundary conditions for the P(\phi)_2 Euclidean field, Ann. Inst. H. Poincaré 25A (1976), 231-334.

[35] Essential self-adjointness for Schrödinger operators with singular potentials, Arch. Ration. Mech. Anal. 52 (1973), 44-48

[36] Ergodic semigroups of positivity preserving self-adjoint operators, J. Funct. Anal. 12 (1973), 335-339

[37] Correlation inequalities and the mass gap in P(\phi)_2, Commun. Math. Phys. 31 (1973), 127-136

[38] Schrödinger operators with singular magnetic vector potentials, Math. Z. 131 (1973), 361-370

[39] (with E. Lieb) Thomas-Fermi theory revisited, Phys. Rev. Lett. 31 (1973), 681-683

[40] (with R. Griffiths) Griffiths-Hurst-Sherman inequalities and a Lee-Yang theorem for the (\phi^4)_2 field theory, Phys. Rev. Lett. 30 (1973), 931-933

[41] Quadratic forms and Klauder's phenomenon: A remark on very singular perturbations, J. Funct. Anal. 14 (1973), 295-298

[42] Positivity of the Hamiltonian semigroup and the construction of Euclidean region fields, Helv. Phys. Acta 46 (1973), 686-696

[43] Pointwise bounds on eigenfunctions and wave packets in N-body quantum systems, I, Proc. Amer. Math. Soc. 42 (1974), 395-401

[44] Absence of positive eigenvalues in a class of multiparticle quantum systems, Math. Ann. 207 (1974), 133-138

[45] (with E. Lieb) On solutions of the Hartree-Fock problem for atoms and molecules, J. Chem. Phys. 61 (1974), 735-736

[46] Pointwise bounds on eigenfunctions and wave packets in N-body quantum systems, II, Proc. Amer. Math. Soc. 45 (1974), 454-456

[47] (with R. Griffiths) The (\phi^4)_2 field theory as a classical Ising model, Commun. Math. Phys. 33 (1973), 145-164

[48] Correlation inequalities and the mass gap in P(\phi)_2, II. Uniqueness of the vacuum for a class of strongly coupled theories, Ann. of Math. 101 (1975), 260-267

[49] (with F. Guerra and L. Rosen) The pressure is independent of the boundary conditions in P(\phi)_2, Bull. Amer. Math. Soc. 80 (1974), 1205-1209

[50] (with F. Guerra and L. Rosen) Correlation inequalities and the mass gap in P(\phi)_2, III. Mass gap for a class of strongly coupled theories with nonzero external field, Commun. Math. Phys. 41 (1975, 19-32

[51] Pointwise bounds on eigenfunctions and wave packets in N-body quantum systems, III, Trans. Amer. Math. Soc. 208 (1975), 317-329

[52] (with J. Rosen) Global support properties of stationary ergodic processes, Duke Math. J. 42 (1975), 51-55

[53] (with E. Lieb) The Thomas-Fermi theory of atoms, molecules and solids, Adv. in Math. 23 (1977), 22-116.

[54] (with J. Rosen) Fluctuations in P(\phi)_1  processes, Ann. Prob. 4 (1976), 155-174

[55] (with E. Lieb) The Hartree-Fock theory for Coulomb systems, Commun. Math. Phys. 53 (1977), 185-193

[56] Existence of the scattering matrix for the linearized Boltzmann equation, Commun. Math. Phys. 41 (1975), 99-108

[57] Operator theory needed in quantum statistical mechanics in boxes, pp. 389-398, Appendix B, in E. Lieb and J. Lebowitz, The constitution of matter, Adv. in Math. 9 (1972), 316-398

[58] Convergence theorems for entropy, Appendix to E. Lieb and M. Ruskai, Proof of the strong subadditivity of quantum mechanical entropy, J. Math. Phys. 14 (1973), 1938-1941

[59] (with W. Faris) Degenerate and non-degenerate ground states for Schrödinger operators, Duke Math. J. 42 (1975), 559-567

[60] (with E. Seiler) An inequality among determinants, Proc. Natl. Acad. Sc. 72 (1975), 3277-3278

[61] (with E. Seiler) On finite mass renormalizations in the two-dimensional Yukawa model, J. Math. Phys. 16 (1975), 2289-2293

[62] (with E. Seiler) Bounds in the Yukawa_2 quantum field theory: Upper bound on the pressure, Hamiltonian bound and linear lower bound, Commun. Math. Phys. 45 (1975), 99-114

[63] (with E. Seiler) Nelson's symmetry and all that in the Yukawa_2 and \phi^4_3 field theories, Ann. Phys. 97 (1976), 470-518

[64] (with J. Fröhlich and T. Spencer) Phase transitions and continuous symmetry breaking, Phys. Rev. Lett. 36 (1976), 804-806

[65] (with J. Fröhlich and T. Spencer) Infrared bounds, phase transitions and continuous symmetry breaking, Commun. Math. Phys. 50 (1976), 79-85

[66] Universal diamagnetism of spinless bose systems, Phys. Rev. Lett. 36 (1976), 1083-1084

[67] (with F.J. Dyson and E. Lieb) Phase transitions in the quantum Heisenberg model, Phys. Rev. Lett. 37 (1976), 120-123

[68] (with F.J. Dyson and E. Lieb) Phase transitions in quantum spin systems with isotropic and non-isotropic interactions, J. Statist. Phys. 18 (1978), 335-383

[69] A remark on Nelson's best hypercontractive estimates, Proc. Amer. Math. Soc. 55 (1976), 376-378

[70] The bound state of weakly coupled Schrödinger operators in one and two dimensions, Ann. Phys. 97 (1976), 279-288

[71] (with P. Deift) On the decoupling of the finite singularities from the question of asymptotic completeness in two body quantum systems, J. Funct. Anal. 23 (1976), 218-238

[72] On the absorption of eigenvalues by continuous spectrum in regular perturbation problems, J. Funct. Anal. 25 (1977), 338-344

[73] Analysis with weak trace ideals and the number of bound states of Schrödinger operators, Trans. Amer. Math. Soc. 224 (1976), 367-380

[74] Notes on infinite determinants of Hilbert space operators, Adv. in Math. 24 (1977), 244-273

[75] On the genericity of nonvanishing instability intervals in Hill's equation, Ann. Inst. H. Poincaré A24 (1976), 91-93

[76] An abstract Kato's inequality for generators of positivity preserving semigroups, Indiana Math. J. 26 (1977), 1067-1073

[77] (with J. Fröhlich) Pure states for general P(\phi)_2 theories: Construction, regularity and variational equality, Ann. of Math. 105 (1977), 493-526

[78] (with M. Reed) The scattering of classical waves from inhomogeneous media, Math. Z. 155 (1977), 163-168

[79] (with J. Avron) Analytic properties of band functions, Ann. Phys. 110 (1978), 85-110

[80] (with R. Blankenbecler and M.L. Goldberger) The bound states of weakly coupled long-range one-dimensional quantum Hamiltonians, Ann. Phys. 108 (1977), 69-78

[81] A canonical decomposition for quadratic forms with applications to monotone convergence theorems, J. Funct. Anal. 28 (1978), 377-385

[82] Lower semicontinuity of positive quadratic forms, Proc. Roy. Soc. Edin. 29 (1977), 267-273

[83] (with P. Deift) A time-dependent approach to the completeness of multiparticle quantum systems, Commun. Pure Appl. Math. 30 (1977), 573-583

[84] Geometric methods in multiparticle quantum systems, Commun. Math. Phys. 55 (1977), 259-274

[85] N-body scattering in the two-cluster region, Commun. Math. Phys. 58 (1978), 205-210

[86] Kato's inequality and the comparison of semi-groups, J. Funct. Anal. 32 (1979), 97-101

[87] (with J. Avron and I. Herbst) The Zeeman effect revisited, Phys. Lett. 62A (1977), 214-216

[88] (with J. Avron and I. Herbst) Formation of negative ions in magnetic fields, Phys. Rev. Lett. 39 (1977), 1068-1070

[89] (with J. Avron and I. Herbst) Schrödinger operators with magnetic fields, I. General interactions, Duke Math. J. 45 (1978), 847-883

[90] (with J. Avron and I. Herbst) Schrodinger operators with magnetic fields, II. Separation of center of mass in homogeneous magnetic fields, Ann. Phys. 114 (1978), 431-451

[91] (with J. Avron and I. Herbst) Schrödinger operators in magnetic fields, III. Atoms in homogeneous magnetic field, Commun. Math. Phys. 79 (1981), 529-572

[92] (with J. Avron and I. Herbst) Schrödinger operators in magnetic fields, IV. Strongly bound states of hydrogen in intense magnetic field, Phys. Rev. A20 (1979), 2287-2296

[93] (with J. Fröhlich, R. Israel and E. Lieb) Phase transitions and reflection positivity, I. General theory and long range interactions, Commun. Math. Phys. 62 (1978), 1-34

[94] (with J. Fröhlich, R. Israel and E. Lieb) Phase transitions and reflection positivity, II. Lattice systems with short-range and Coulomb interactions, J. Statist. Phys. 22 (1980), 297-341

[95] (with P. Deift, W. Hunziker and E. Vock) Pointwise bounds on eigenfunctions and wave packets in N-body quantum systems, IV, Commun. Math. Phys. 64 (1978), 1-34

[96] Scattering theory and quadratic forms: On a theorem of Schechter, Commun. Math. Phys. 53 (1977), 151-153

[97] (with E. Lieb) Monotonicity of the electronic contribution of the Born-Oppenheimer energy, J. Phys. B11 (1978), L537-542

[98] Maximal and minimal Schrödinger forms, J. Oper. Th. 1 (1979), 37-47

[99] (with E.B. Davies) Scattering theory for systems with different spatial asymptotics on the left and right, Commun. Math. Phys. 63 (1978), 277-301

[100] (with I. Herbst) Stark effect revisited, Phys. Rev. Lett. 41 (1978), 67-69

[101] (with I. Herbst) Some remarkable examples in eigenvalue perturbation theory, Phys. Lett. 78B (1978), 304-306

[102] (with I. Herbst) Dilation analyticity in constant electric field, II. The N-body problem, Borel summability, Commun. Math. Phys. 80 (1981), 181-216

[103] (with C. Radin) Invariant domains for the time-dependent Schrödinger equation, J. Diff. Eqn. 29 (1978), 289-296

[104] (with L. Benassi, V. Grecchi and E. Harrell) Bender-Wu formula and the Stark effect in hydrogen, Phys. Rev. Lett. 42 (1979), 704-707

[105] (with E. Harrell) The mathematical theory of resonances whose widths are exponentially small, Duke Math. J. 47 (1980), 845-902

[106] Phase space analysis of simple scattering systems. Extensions of some work of Enss, Duke Math. J. 46 (1979), 119-168

[107] The definition of molecular resonance curves by the method of exterior complex scaling, Phys. Lett. 71A (1979), 211-214

[108] (with J. Morgan) Behavior of molecular potential energy curves for large nuclear separations, Intl. J. Quan. Chem. 17 (1980), 1143-1166

[109] (with M. Schechter) Unique continuation for Schrödinger operators with unbounded potentials, J. Math. Anal. Appl. 77 (1980), 482-492

[110] Brownian motion, Lp properties of Schrödinger operators and the localization of binding, J. Funct. Anal. 35 (1980), 215-229

[111] (with S. Graffi and V. Grecchi) Complete separability of the Stark effect in hydrogen, J. Phys. A12 (1979), L193-L197

[112] A remark on Dobrushin's uniqueness theorem, Commun. Math. Phys. 68 (1979), 183-185

[113] The classical limit of quantum partition functions, Commun. Math. Phys. 71 (1980), 247-276

[114] (with M. Klaus) Binding of Schrödinger particles through conspiracy of potential wells, Ann. Inst. H. Poincaré A30 (1979), 83-87

[115] (with M. Klaus) Coupling constant thresholds in nonrelativistic quantum mechanics, I. Short range two-body case, Ann. Phys. 130 (1980), 251-281

[116] (with A. Alonso) The Birman-Krein-Vishik theory of self-adjoint extensions of semibounded operators, J. Oper. Th. 4 (1980), 251-270

[117] (with J. Avron) A counterexample to the paramagnetic conjecture, Phys. Lett. 75A (1979), 41-42

[118] Mean field upper bound on the transition temperature in multicomponent ferromagnets, J. Statist. Phys. 22 (1980), 491-493

[119] (with M. Hoffmann-Ostenhof and T. Hoffmann-Ostenhof) On the nodal structure of atomic eigenfunctions, J. Phys. A13 (1980), 1131-1133

[120] (with M. Hoffmann-Ostenhof and T. Hoffmann-Ostenhof) Brownian motion and a consequence of Harnack's inequality: Nodes of quantum wave functions, Proc. Amer. Math. Soc. 80 (1980), 301-305

[121] (with J. Morgan) The calculation of molecular resonances by complex scaling, J. Phys. B14 (1981), L167-L171

[122] (with M. Klaus) Coupling constant threshold in non-relativistic quantum mechanics, II. Two-cluster thresholds in N-body systems, Commun. Math. Phys. 78 (1980), 153-168

[124] (with V. Enss) Bounds on total cross-sections in atom-atom and atom-ion collisions by geometric methods, Phys. Rev. Lett. 44 (1980), 319-321

[125] (with V. Enss) Finite total cross-sections in non-relativistic quantum mechanics, Commun. Math. Phys. 76 (1980), 177-210

[126] Decay of correlations in ferromagnets, Phys. Rev. Lett. 44 (1980), 547-549

[127] Correlation inequalities and the decay of correlations in ferromagnets, Commun. Math. Phys. 77 (1980), 111-126

[128] (with M. Aizenman) Local Ward identities and the decay of correlations in ferromagnets, Commun. Math. Phys. 77 (1980), 137-143

[129] (with M. Aizenman) A comparison of plane rotor Ising models, Phys.  Lett. A 76 (1980), 281-282

[130] (with K. Miller) Quantum magnetic Hamiltonians with remarkable spectral properties, Phys. Rev. Lett. 44 (1980), 1706-1707

[131] (with P. Perry and I. Sigal) Absence of singular continuous spectrum in N-body quantum systems, Bull. Amer. Math. Soc. 3 (1980), 1019-1024

[132] (with P. Perry and I. Sigal) Spectral analysis of N-body Schrödinger operators, Ann. of Math. 114 (1981), 519-567

[133] (with R. Carmona) Pointwise bounds on eigenfunctions and wave packets in N-body quantum systems, V. Lower bounds and path integrals, Commun. Math. Phys. 80 (1981), 59-98

[134] (with E. Lieb) Pointwise bounds on eigenfunctions and wave packets in N-body quantum systems, VI. Asymptotics in the two-cluster region, Adv. Appl. Math. 1 (1980), 324-343

[135] (with M. Aizenman) Brownian motion and Harnack's inequality for Schrödinger operators, Commun. Pure Appl. Math. 35 (1982), 209-273

[136] Large time behavior of the Lp norm of Schrödinger semigroups, J. Funct. Anal. 40 (1981), 66-83

[137] Spectrum and continuum eigenfunctions of Schrödinger operators, J. Funct. Anal. 42 (1981), 347-355

[138] Convergence in trace ideals, Proc. Amer. Math. Soc. 83 (1981), 39-43  [146]

[139] (with A. Sokal) Rigorous entropy-energy arguments, J. Statist. Phys. 25 (1981), 679-694

[140] Pointwise domination of matrices and comparison of I_p norms, Pacific J. Math. 97 (1981), 471-475

[141] (with J. Avron) The asymptotics of the gap in the Mathieu equation, Ann. Phys. 134 (1981), 76-84

[142] (with J. Avron) Transient and recurrent spectrum, J. Funct. Anal. 43 (1981), 1-31

[143] The rate of falloff of Ising model correlations at large temperature, J. Statist. Phys. 26 (1981), 53-58

[144] Absence of continuous symmetry breaking in a one-dimensional n-2 model, J. Statist. Phys. 26 (1981), 307-311

[145] (with S. Friedland) The codimension of degenerate pencils, Linear Alg. Appl. 44 (1982), 41-53

[146] (with J. Avron) Almost periodic Hill's equation and the rings of Saturn, Phys. Rev. Lett. 46 (1981), 1166-1168

[147] (with J. Avron) Almost periodic Schrödinger operators, I. Limit periodic potentials, Commun. Math. Phys. 82 (1982), 101-120

[148] (with J. Avron) Singular continuous spectrum for a class of almost periodic Jacobi matrices, Bull. Amer. Math. Soc. 6 (1982), 81-85

[149] (with J. Avron) Almost periodic Schrödinger operators, II. The integrated density of states, Duke Math. J. 50 (1983), 369-391

[150] Hardy and Rellich inequalities in non-integral dimension, J. Oper. Th. 9 (1983), 143-146   Addendum, J. Oper. Th. 12 (1984), 197

[151] Continuity of the density of states in magnetic field, J. Phys. A15 (1982), 2981-2983

[152] (with J. Bellissard) Cantor spectrum for the almost Mathieu equation, J. Funct. Anal. 48 (1982), 408-419

[153] (with L. Yaffe) Rigorous perimeter law upper bound on Wilson loops, Phys. Lett. 115B (1982), 145-147

[154] (with E. Harrell) Schrödinger operator methods in the study of a certain nonlinear PDE, Proc. Amer. Math. Soc. 88 (1983), 376-377

[155] (with W. Craig) Subharmonicity of the Lyaponov index, Duke Math. J. 50 (1983), 551-560

[156] (with N. Corngold and E. Harrell) The mathematical theory of resonances whose widths are exponentially small, II, J. Math. Anal. Appl. 99 (1984), 447-457

[157] Some Jacobi matrices with decaying potential and dense point spectrum, Commun. Math. Phys. 87 (1982), 253-258

[158] Some quantum operators with discrete spectrum but classically continuous spectrum, Ann. Phys. 146 (1983), 209-220

[159] Nonclassical eigenvalue asymptotics, J. Funct. Anal. 53 (1983), 84-98

[160] (with M. Hoffmann-Ostenhof and T. Hoffmann-Ostenhof) A multiparticle Coulomb system with bound state at threshold, J. Phys. A16 (1983), 1125-1131

[161] Semiclassical analysis of low lying eigenvalues, I. Non-degenerate minima: Asymptotic expansions, Ann. Inst. H. Poincaré 38 (1983), 295-307

[162] Semiclassical analysis of low lying eigenvalues, II. Tunneling, Ann. of Math. 120 (1984), 89-118

[163] Instantons, double wells and large deviations, Bull. Amer. Math. Soc. 8 (1983), 323-326

[164] Equality of the density of states in a wide class of tight binding Lorentzian models, Phys. Rev. B27 (1983), 3859-3860

[165] (with F. Bentosela, R. Carmona, P. Duclos, B. Souillard and R. Weder) Schrödinger operators with electric field and random or deterministic potential, Commun. Math. Phys. 88 (1983), 387-397

[166] (with W. Craig) Log Hölder continuity of the integrated density of states for stochastic Jacobi matrices, Commun. Math. Phys. 90 (1983), 207-218

[167] (with J. Avron and W. Craig) Large coupling behavior of the Lyaponov exponent for tight binding one dimensional random systems, J. Phys. A16 (1983), L209-L211

[168] Kotani theory for one dimensional stochastic Jacobi matrices, Commun. Math. Phys. 89 (1983), 227-234

[169] (with P. Deift) Almost periodic Schrödinger operators, III. The absolutely continuous spectrum in one dimension, Commun. Math. Phys. 90 (1983), 389-411

[170] Almost periodic Schrödinger operators, IV. The Maryland model, Ann. Phys. 159 (1985), 157-183

[171] (with J. Avron and R. Seiler) Homotopy and quantization in condensed matter physics, Phys. Rev. Lett. 51 (1983), 51-53

[172] Holonomy, the quantum adiabatic theorem and Berry's phase, Phys. Rev. Lett. 51 (1983), 2167-2170

[173] (with E.B. Davies) Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians, J. Funct. Anal. 59 (1984), 335-395

[174] Semiclassical analysis of low lying eigenvalues, III. Width of the ground state band in strongly coupled solids, Ann. Phys. 158 (1984), 415-420

[175] (with E. Lieb, I. Sigal and W. Thirring) Asymptotic neutrality of large Z ions, Phys. Rev. Lett. 52 (1984), 994-996

[176] (with F. Delyon and B. Souillard) From power localized to extended states in a class of one-dimensional disordered systems, Phys. Rev. Lett. 52 (1984), 2187-2189

[177] Semiclassical analysis of low lying eigenvalues, IV. The flea on the elephant, J. Funct. Anal. 63 (1985), 123-136

[178] (with F. Delyon and B. Souillard) From power pure point to continuous spectrum in disordered systems, Ann. Inst. H. Poincaré 42 (1985), 283-309

[179] (with W. Kirsch) Universal lower bounds on eigenvalue splittings for one dimensional Schrödinger operators, Commun. Math. Phys. 97 (1985), 453-460

[180] (with W. Kirsch) Lifshitz tails for periodic plus random potentials, J. Statist. Phys. 42 (1986), 799-808

[181] (with W. Kirsch) Comparison theorems for the gap of Schrödinger operators, J. Funct. Anal. 75 (1987), 396-410

[182] (with W. Kirsch and S. Kotani) Absence of absolutely continuous spectrum for some one dimensional random but deterministic Schrödinger operators, Ann. Inst. H. Poincaré 42 (1985), 383-406

[183] (with J. Avron) Stability of gaps for periodic potentials under variation of the magnetic field, J. Phys. A18 (1985), 2199-2205

[184] (with F. Gesztesy and B. Thaller) On the self-adjointness of Dirac operators with anomalous magnetic moment, Proc. Amer. Math. Soc. 94 (1985), 115-118

[185] Schrödinger semigroups on the scale of Sobolev spaces, Pacific J. Math. 122 (1986), 475-480

[186] (with E.B. Davies) L1-properties of intrinsic Schrödinger semigroups, J. Funct. Anal. 65 (1986), 126-146

[187] (with M. Taylor and T. Wolff) Some rigorous results for the Anderson model, Phys. Rev. Lett. 54 (1985), 1589-1592

[188] (with M. Taylor) Harmonic analysis on SL(2, R) and smoothness of the density of states in the one dimensional Anderson model, Commun. Math. Phys. 101 (1985), 1-19

[189] (with T. Wolff) Singular continuous spectrum under rank one perturbations and localization for random Hamiltonians, Commun. Pure Appl. Math. 39 (1986), 75-90

[190] Localization in general one dimensional random systems, I. Jacobi matrices, Commun. Math. Phys. 102 (1985), 327-336

[191] Internal Lifschitz tails, J. Statist. Phys. 46 (1987), 911-918

[192] (with S. Kotani) Localization in general one-dimensional random systems, II. Continuum Schrödinger operators, Commun. Math. Phys. 112 (1987), 103-119

[193] (with D. Bolle, F. Gesztesy and H. Grosse) Krein's spectral shift function and Fredholm determinants as efficient methods to study supersymmetric quantum mechanics, Lett. Math. Phys. 13 (1987), 127-133

[194] (with F. Delyon and B. Souillard) Localization for off-diagonal disorder and for continuous Schrödinger operators, Commun. Math. Phys. 109 (1987), 157-165

[195] (with D. Bolle, F. Gesztesy and H. Grosse) Witten index, axial anomaly and Krein's spectral shift function in supersymmetric quantum mechanics, J. Math. Phys. 28 (1987), 1512-1525

[196] (with E.B. Davies and M. Taylor) Lp spectral theory of Kleinian groups, J. Funct. Anal. 78 (1988), 116-136

[197] (with F. Gesztesy) Topological invariance of the Witten index, J. Funct. Anal. 79 (1988), 91-103

[198] (with S. Kotani) Stochastic Schrödinger operators and Jacobi matrices on the strip, Commun. Math. Phys. 119 (1988), 403-429

[199] (with E. Lieb, I. Sigal and W. Thirring) Approximate neutrality of large-Z ions, Commun. Math. Phys. 116 (1988), 635-644

[200] (with F. Gesztesy) On a theorem of Deift and Hempel, Commun. Math. Phys. 116 (1988), 503-505

[201] (with W. Kirsch) Corrections to the classical behavior of the number of bound states of Schrödinger operators, Ann. Phys. 183 (1988), 122-130

[202] (with H. Englisch, M. Schroder and W. Kirsch) Density of surface states in discrete models, Phys. Rev. Lett. 61 (1988), 1261-1262

[203] (with F. Gesztesy, D. Gurarie, H. Holden, M. Klaus, L. Sadun and P. Vogl) Trapping and cascading of eigenvalues in the large coupling limit, Commun. Math. Phys. 118 (1988), 597-634

[204] (with J. Avron, L. Sadun and J. Segert) Topological invariants in Fermi systems with time-reversal invariance, Phys. Rev. Lett. 61 (1988), 1329-1332

[205] (with J. Avron, L. Sadun and J. Segert) Chern numbers and Berry's phases in Fermi systems, Commun. Math. Phys. 124 (1989), 595-627

[206] (with F. Gesztesy) Constructing solutions of the mKdV-equation, J. Funct. Anal. 89 (1990) 53-60

[207] (with H. Englisch, M. Schroder and W. Kirsch) Random Hamiltonains ergodic in all but one direction, Commun. Math. Phys. 128 (1990), 613-625

[208] (with T. Spencer) Trace class perturbations and the absence of absolutely continuous spectra, Commun. Math. Phys. 125 (1989), 113-125

[209] (with J. Avron and J. Howland) Adiabatic theorems for dense point spectrum, Commun. Math. Phys. 128 (1990), 497-507

[210] (with R. Carmona and W. Masters) Relativistic Schrödinger operators: Asymptotic behavior of the eigenfunctions, J. Funct. Anal. 91 (1990), 117-142

[211] (with J. Avron and P. van Mouche) On the measure of the spectrum for the almost Mathieu operator, Commun. Math. Phys. 132 (1990), 103-118

[212] (with E.B. Davies) Spectral properties of the Neumann Laplacian of horns, Geom. Funct. Anal. 2 (1992), 105-117

[213] (with F. Gesztesy and W. Schweiger) Commutation methods applied to the mKdV-equation, Trans. Amer. Math. Soc. 324 (1991), 465-525

[214] (with F. Gesztesy, H. Holden and E. Saab) Explicit construction of solutions of the modified Kadomtsev-Petviashvili equation, J. Funct. Anal. 98 (1991), 211-228

[215] (with F. Gesztesy) A short proof of Zheludev's theorem, Trans. Amer. Math. Soc. 335 (1993), 329-340

[216] (with J. Avron and R. Seiler) The quantum Hall effect and the relative index for projections, Phys. Rev. Lett. 65 (1990), 2185-2188

[217] (with R. Hempel and L. Seco) The essential spectrum of Neumann Laplacians on some bounded singular domains, J. Funct. Anal. 102 (1991), 448-483

[218] Absence of ballistic motion, Commun. Math. Phys. 134 (1990) 209-212

[219] (with E.B. Davies) Lp-norms of non-critical Schrödinger semigroups, J. Funct. Anal. 102 (1991), 95-115

[220] Best constants to some operator smoothness estimates, J. Funct. Anal. 107 (1992), 66-71

[221] The Neumann Laplacian of a jelly roll, Proc. Amer. Math. Soc. 114 (1992), 783-785

[222] The Weyl transform and Lp functions on phase space, Proc. Amer. Math. Soc. 116 (1992), 1045-1047

[223] Large time behavior of the heat kernel: On a theorem of Chavel and Karp, Proc. Amer. Math. Soc. 118 (1993), 513-514

[224] (with F. Gesztesy, H. Holden and Z. Zhao) On the Toda and Kac-van Moerbeke systems, Trans. Amer. Math. Soc. 339 (1993), 849-868

[225] (with V. Jaksic and S. Molchanov) Eigenvalue asymptotics of the Neumann Laplacian of regions and manifolds with cusps, J. Funct. Anal. 106 (1992), 59-79

[226] (with F. Gesztesy and G.M. Graf) The ground state energy of Schrödinger operators, Commun. Math. Phys. 150 (1992), 375-384

[227] (with G.M. Graf) Asymptotic series for the ground state energy of Schrödinger operators, J. Funct. Anal. 112 (1993), 442-446

[228] (with J. Avron and R. Seiler) Charge deficiency, charge transport and comparison of dimensions, Commun. Math. Phys. 159 (1994), 399-422

[229] (with J. Avron and R. Seiler) The index of a pair of projections, J. Funct. Anal. 120 (1994), 220-237

[230] (with F. Gesztesy, H. Holden and Z. Zhao) Trace formulae and inverse spectral theory for Schrödinger operators, Bull. Amer. Math. Soc. 29 (1993), 250-255

[231] (with A. Gordon, V. Jaksic and S. Molchanov) Spectral properties of random Schrödinger operators with unbounded potentials, Commun. Math. Phys. 157 (1993), 23-50

[232] Cyclic vectors in the Anderson model, Rev. Math. Phys. 6 (1994), 1183-1185

[233] (with R. del Rio, S. Jitomirskaya and N. Makarov) Singular continuous spectrum is generic, Bull. Amer. Math. Soc. 31 (1994), 208-212

[234] Operators with singular continuous spectrum: I. General operators, Ann. of Math. 141 (1995), 131-145

[235] (with R. del Rio and N. Makarov) Operators with singular continuous spectrum: II. Rank one operators, Commun. Math. Phys. 165 (1994), 59-67

[236] (with S. Jitomirskaya) Operators with singular continuous spectrum: III. Almost periodic Schrödinger operators, Commun. Math. Phys. 165 (1994), 201-205

[237] (with F. Gesztesy and H. Holden) Absolute summability of the trace relation for certain Schrödinger operators, Commun. Math. Phys. 168 (1995), 137-161

[238] (with F. Gesztesy) Rank one perturbations at infinite coupling, J. Funct. Anal. 128 (1995), 245-252

[239] (with F. Gesztesy, H. Holden and Z. Zhao) Higher order trace relations for Schrödinger operators, Rev. Math. Phys. 7 (1995), 893-922

[240] (with F. Gesztesy, H. Holden and Z. Zhao) A trace formula for multidimensional Schrödinger operators, J. Funct. Anal. 141 (1996), 449-465

[241] (with F. Gesztesy) The xi function, Acta Math., 176 (1996), 49-71

[242] Lp norms of the Borel transform and the decomposition of measures, Proc. Amer. Math. Soc. 123 (1995), 3749-3755

[243] (with R. del Rio and G. Stolz) Stability of spectral types for Sturm-Liouville operators, Math. Research. Lett. 1 (1994), 437-450

[244] (with A. Kiselev) Rank one perturbations with infinitesimal coupling, J. Funct. Anal. 130 (1995), 345-356

[245] (with A. Hof and O. Knill) Singular continuous spectrum for palindromic Schrödinger operators, Commun. Math. Phys. 174 (1995), 149-159

[246] Operators with singular continuous spectrum, VI. Graph Laplacians and Laplace-Beltrami operators, Proc. Amer. Math. Soc. 124 (1996), 1177-1182

[247] (with G. Stolz) Operators with singular continuous spectrum, V. Sparse potentials, Proc. Amer. Math. Soc. 124 (1996), 2073-2080

[248] Operators with singular continuous spectrum, VII. Examples with borderline time decay, Commun. Math. Phys. 176 (1996), 713-722

[249] (with F. Gesztesy) Uniqueness theorems in inverse spectral theory for one-dimensional Schrödinger operators, Trans. Amer. Math. Soc. 348 (1996), 349-373

[250] (with R. del Rio, S. Jitomirskaya and Y. Last) Operators with singular continuous spectrum, IV. Hausdorff dimensions, rank one perturbations, and localization, J. d'Analyse Math. 69 (1996), 153-200

[251] (with R. del Rio, S. Jitomirskaya and Y. Last) What is localization?, Phys. Rev. Lett. 75 (1995), 117-119

[252] (with F. Gesztesy and G. Teschl) Zeros of the Wronskian and renormalized oscillation theory, Am. J. Math. 118 (1996), 571-594

[253] Bounded eigenfunctions and absolutely continuous spectra for one-dimensional Schrödinger operators, Proc. Amer. Math. Soc. 124 (1996), 3361-3369

[254] Some Schrödinger operators with dense point spectrum, Proc. Amer. Math. Soc. 125 (1997), 203-208

[255] (with W. Bulla, F. Gesztesy and W. Renger) Weakly coupled bound states in quantum waveguides, Proc. Amer. Math. Soc. 125 (1997), 1487-1495

[256] (with Y.F. Zhu) The Lyapunov exponents for Schrödinger operators with slowly oscillating potentials, J. Funct. Anal. 140 (1996), 541-556

[257] (with A. Gordon, S. Jitomirskaya and Y. Last) Duality and singular continuous spectrum in the almost Mathieu equation, Acta Math. 178 (1997), 169-183

[258] (with F. Gesztesy and G. Teschl) Spectral deformations of one-dimensional Schrödinger operators, J. d'Analyse Math. 70 (1996), 267-324

[259] (with R. del Rio) Point spectrum and mixed spectral types for rank one perturbations, Proc. Amer. Math. Soc. 125 (1997), 3593-3599

[260] (with F. Gesztesy) Inverse spectral analysis with partial information on the potential, I. The case of an a.c. component in the spectrum, Helv. Phys. Acta 70 (1997), 66-71

[261] (with F. Gesztesy) m-functions and inverse spectral analysis for finite and semi-infinite Jacobi matrices, J. d'Analyse Math. 73 (1997), 267-297

[262] Spectral averaging and the Krein spectral shift, Proc. Amer. Math. Soc. 126 (1998), 1409-1413

[263] (with Y. Last) Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schrödinger operators, Invent. math. 135 (1999), 329-367

[264] (with F. Gesztesy) Inverse spectral analysis with partial information on the potential, II. The case of discrete spectrum, Trans. Amer. Math. Soc. 352 (2000), 2765-2787

[265] (with A. Kiselev and Y. Last) Modified Prüfer and EFGP transforms and the spectral analysis of one-dimensional Schrödinger operators, Commun. Math. Phys. 194 (1998), 1-45.

[266] (with R. del Rio and F. Gesztesy) Inverse spectral analysis with partial information on the potential, III. Updating boundary conditions, Intl. Math. Research Notices, (1997) no. 15, 751-758

[267] (with Y. Last) Modified Prüfer and EFGP transforms and deterministic models with dense point spectrum, J. Funct. Anal. 154 (1998), 513-530

[268] (with F. Gesztesy) On the determination of a potential from three spectra, Amer. Math. Soc. Transl. (2) 189 (1999), 85-92

[269] (with A. Kiselev and C. Remling) Effective perturbation methods for one-dimensional Schrödinger operators, J. Diff. Eq. 151 (1999), 290-312

[270] The classical moment problem as a self-adjoint finite difference operator, Advances in Math. 137 (1998), 82-203

[271] A new approach to inverse spectral theory, I. Fundamental formalism, Ann. of Math. 150 (1999), 1029-1057

[272] (with F. Gesztesy) A new approach to inverse spectral theory, II. General real potentials and the connection to the spectral measure, Ann. of Math. 152 (2000), 593-643

[273] (with A. Ramm) A new approach to inverse spectral theory, III. Short-range potentials, J. d'Analyse Math. 80 (2000), 319-334

[274] A Feynman-Kac formula for unbounded semigroups, Intl. Conference on Infinite Dimensional (Stochastic) Analysis and Quantum Physics, Leipzig 1999, Canadian Math. Soc. Conf. Proc. 28 (2000), 317-321

[275] (with F. Gesztesy) On local Borg-Marchenko uniqueness results, Commun. Math. Phys. 211 (2000), 273-287

[276] Resonances in one dimension and Fredholm determinants, J. Funct. Anal. 178 (2000), 396-420

[277] (with D. Hundertmark) An optimal Lp-bound on the Krein spectral shift function, J. d'Analyse Math. 87 (2002), 199-208 (volume dedicated to the memory of Tom Wolff)

[278] (with W. Kirsch) Approach to equilibrium for a forced Burgers equation, Journal of Evolution Equations 1 (2001), 411-419

[279] (with A. Kiselev and Y. Last) Stability of singular spectral types under decaying perturbations, J. Funct. Anal. 198 (2003), 1-27

[280] (with D. Hundertmark) Lieb-Thirring inequalities for Jacobi matrices, J. Approx. Theory 118 (2002), 106-130

[281] (with R. Killip) Sum rules for Jacobi matrices and their applications to spectral theory, Ann. of Math. 158 (2003), 253-321.

[282] (with A. Zlatos) Sum rules and the Szego condition for orthogonal polynomials on the real line, Commun. Math. Phys. 242 (2003), 393-423.

[283] (with S. Denisov) Zeros of orthogonal polynomials on the real line, J. Approx. Theory 121 (2003), 357-364.

[284] (with D. Damanik and D. Hundertmark) Bound states and the Szegö condition for Jacobi matrices and Schrödinger operators, J. Funct. Anal. 205 (2003), 357-379

[285] (with D. Damanik, D. Hundertmark, and R. Killip) Variational estimates for discrete Schrödinger operators with potentials of indefinite sign, Commun. Math. Phys. 238 (2003), 545-562.

[286] (with D. Hundertmark) A diamagnetic inequality for semigroup differences, J. Reine Angew. Math. 571 (2004), 107-130.

[287] The Golinskii-Ibragimov method and a theorem of Damanik-Killip, Int. Math. Res. Not. (2003), no. 36, 1973-1986.

[288] A canonical factorization for meromorphic Herglotz functions on the unit disk and sum rules for Jacobi matrices, J. Funct. Anal. 214 (2004), 396-409

[289] (with F. Gesztesy) Connectedness of the isospectral manifold for one-dimensional half-line Schrödinger operators, J. Statist. Phys. 116 (2004), 361-365

[290] Ratio asymptotics and weak asymptotic measures for orthogonal polynomials on the real line, J. Approx. Theory 126 (2004), 198-217

[291] (with D. Damanik and R. Killip) Necessary and sufficient conditions in the spectral theory of Jacobi matrices and Schrödinger operators, Int. Math. Res. Not. (2004), no. 22, 1087-1097

[292] (with V. Totik) Limits of zeros of orthogonal polynomials on the circle, Math. Nachr. 278 (2005), 1615-1620 (issue in honor of F.V. Atkinson)

[293] On a theorem of Kac and Gilbert, J. Funct. Anal. 223 (2005), 109-115

[294] Orthogonal polynomials on the unit circle: New results, Int. Math. Res. Not. (2004), no. 53, 2837-2880

[295] (with D. Damanik and R. Killip) Schrödinger operators with few bound states, Comm. Math. Phys. 258 (2005), 741-750

[296] (with A. Zlatos) Higher-order Szego theorems with two singular points, J. Approx. Theory 134 (2005), 114-129

[297] Aizenman's theorem for orthogonal polynomials on the unit circle, Const. Approx. 23 (2006), 229-240

[298] Fine structure of the zeros of orthogonal polynomials, I. A tale of two pictures, Electronic Transactions on Numerical Analysis 25 (2006), 328-368

[299] Fine structure of the zeros of orthogonal polynomials, II. OPUC with competing exponential decay, J. Approx. Theory 135 (2005), 125-139

[300] Fine structure of the zeros of orthogonal polynomials, III. Periodic recursion coefficients, Comm. Pure Appl. Math. 59 (2006) 1042-1062

[301] (with D. Damanik) Jost functions and Jost solutions for Jacobi matrices, I. A necessary and sufficient condition for Szegö asymptotics, Invent. Math. 165 (2006), 1-50

[302] (with D. Damanik) Jost functions and Jost solutions for Jacobi matrices, II. Decay and analyticity, Int. Math. Res. Not. 2006, Article ID 19396, 32 pages, 2006.

[303]  Meromorphic Szegö functions and asymptotic series for Verblunsky coefficients, Acta Math. 195 (2005), 267-285

[304]  (with Y. Last) The essential spectrum of Schrödinger, Jacobi, and CMV operators, J. d'Analyse Math. 98 (2006), 183-220

[305]  Meromorphic Jost functions and asymptotic expansion for Jacobi parameters, Funct. Anal. Appl. 41 (2007), 143-153 (volume dedicated to M. Krein)

[306]  (with R. Killip) Sum rules and spectral measures of Schrödinger operators with L2 potentials, Annals of Math. 170 (2009), 739-782.

[307]  (with E.B. Davies)  Eigenvalue estimates for non-normal matrices and the zeros of random orthogonal polynomials on the unit circle, J. Approx. Theory 141 (2006), 189-213

[308]  Rank one perturbations and the zeros of paraorthogonal polynomials on the unit circle, J. Math. Anal. Appl. 329 (2007), 376-382

[309]  (with Y. Last)  Fine structure of the zeros of orthogonal polynomials, IV. A priori bounds and clock behavior, Comm. Pure Appl. Math. 61 (2008), 486-538

[310]  Zeros of OPUC and long time asymptotics of Schur and related flows, Inverse Problems and Imaging 1 (2007), 189-215

[311]  (with M.J. Cantero) Poisson brackets of orthogonal polynomials, J. Approx. Theory 158 (2009), 3-48.

[312]  (with D. Damanik and R. Killip) Perturbations of orthogonal polynomials with periodic recursion coefficients, Annals of Math. 171 (2010), 1931-2010

[313]  (with R. Frank and T. Weidl)  Eigenvalue bounds for perturbations of Schrödinger operators and Jacobi matrices with regular ground states, Comm. Math. Phys. 282 (2008), 199-208

[314]  (with F. Gesztesy and A. Pushnitski) On the Koplienko spectral shift function, I. Basics,  Zh. Mat. Fiz. Anal. Geom. 4  (2008),  no. 1, 63-107

[315]  (with D. Hundertmark) Eigenvalue bounds in the gaps of Schrödinger operators and Jacobi matrices, J. Math. Anal. Appl. 340 (2008), 892-900

[316]  Two extensions of Lubinsky's universality theorem, J. d'Analyse Math. 105 (2008), 345-362

[317]  Equilibrium measures and capacities in spectral theory, Inverse Problems and Imaging 1 (2007), 713-772

[318]  Weak convergence of CD kernels and applications, Duke Math. J. 146 (2009), 305-330

[319]  Regularity and the Cesàro–Nevai class, J. Approx. Theory 156 (2009), 142-153

[320]  (with Y. Kreimer and Y. Last) Monotone Jacobi parameters and non-Szegö weights, J. Approx. Theory 157 (2009), 144-171

[321]  (with J. Breuer and Y. Last) The Nevai condition, Constr. Approx. 32 (2010), 221-254

[322]  Schrödinger operators with purely discrete spectrum, Methods Funct. Anal. Topology 15 (2009), 61-66.

[323] (with J. Christiansen and M. Zinchenko) Finite gap Jacobi matrices, I. The isospectral torus, Constr. Approx. 32 (2010), 1-65

[324] (with A. Avila and Y. Last) Bulk universality and clock spacing of zeros for ergodic Jacobi matrices with a.c. spectrum, Analysis & PDE 3 (2010), 81-108

[325] (with A. Poltoratski and M. Zinchenko) The Hilbert transform of a measure, J. d'Analyse Math. 111 (2010), 247-265

[326] (with J. Breuer and E. Ryckman) Equality of the spectral and dynamical definitions of reflection, Comm. Math. Phys. 295 (2010), 531-550

[327] (with J. Christiansen and M. Zinchenko) Finite gap Jacobi matrices, II. The Szegö class, Constr. Approx. 33 (2011), 365-403

[328] (with J. Breuer) Natural boundaries and spectral theory, Advances in Mathematics 226 (2011), 4902-4920

[329] (with R. Frank) Critical Lieb-Thirring bounds in gaps and the generalized Nevai conjecture for finite gap Jacobi matrices, Duke Math. J. 157 (2011), 461-493

[330]  (with A. Martinez-Finkelshtein) Asymptotics of the L2 norm of derivatives of OPUC, J. Approx. Theory 163 (2011), 747-778

[331]  On the removal of finite discrete spectrum by coefficient stripping, J. Spectr. Theory 1 (2011), 81-85

[332]  (with J. Christiansen and M. Zinchenko) Finite gap Jacobi matrices, III. Beyond the Szegö class, Constr. Approx. 35 (2012), 259-272

[333]  (with J. Breuer and Y. Last) Stability of asymptotics of Christoffel-Darboux kernels, Comm. Math. Phys. 330 (2014), 1155-1178

[334] (with H. Krüger) Cantor polynomials and  some related classes of OPRL, J. Approx. Theory  191 (2015), 71-93

[335] (with R. Frank)  Eigenvalue Bounds for Schrödinger Operators with Complex Potentials. II , J. Specr. Theory, 7  (2017), 633-658

[336]  (with J. Christiansen and M. Zinchenko) Asymptotics of Chebyshev Polynomials, I. Subsets of R.,  Invent. math., 208 (2017), 217-245

[337]  A Cayley-Hamiltonian Theorem for Periodic Finite Band Matrices, Functional analysis and operator theory for quantum physics, ed.  J. Dittrich, H. Kovařík and A. Laptev, EMS Ser. Congr. Rep., Eur. Math. Soc., Zürich ( 2017),  525-529

[338]  (with R. Frank and M. Lemm)  Condensation of fermion pairs in a domain, Calculus of Variations and Partial Differential Equations, 56 (2017) paper 54 (40 pages).

[339]  (with J. Breuer and O. Zeitouni)  Large Deviations and Sum Rules for Spectral Theory - A Pedagogical Approach,  J. Specr. Theory, to appear

[340]  (with J. Breuer and O. Zeitouni)  Large Deviations and the Lukic Conjecture,  Dukr Math. J., 167 (2018), 2857-2902.

[341]  (with J. Christiansen, P. Yuditskii and M. Zinchenko) Asymptotics of Chebyshev Polynomials, II. DCT Subsets of R,  to appear  in Duke Math. J.

[342] Unitaries Permuting Two Orthogonal Projections,  Linear Alg. Appl., 528 (2017), 436-441.

[343] (with A. Böttcher and I. Spitkovsky) Similarity between two projections, Int. Eq. and Op. Th. 89 (2017), 507--518.

[344]  (with J. Christiansen and M. Zinchenko) Asymptotics of Chebyshev Polynomials, III. Sets Saturating Szegő, Schiefermayr, and Totik--Widom Bounds, to appear in Analysis as a Tool in Mathematical Physics - in Memory of Boris Pavlov, ed. P. Kurasov, A. Laptev, S. Naboko and B. Simon, to be published by Birkhauser.

[345] (with A. Martinez--Finkelshtein and B Simanek) Poncelet's Theorem, Paraorthogonal Polynomials and the Numerical Range of Compressed Multiplication Operators, preprint.

[346]  (with J. Christiansen,i and M. Zinchenko) Asymptotics of Chebyshev Polynomials, IV. Comments on the Complex Case,  preprint

### BOOKS AND MONOGRAPHS

[I] Quantum Mechanics for Hamiltonians Defined by Quadratic Forms, in Princeton Series in Physics, Princeton University Press, 1971

[II] (with M. Reed) Methods of Modern Mathematical Physics, Vol. 1: Functional Analysis, Academic Press, 1972  ; second edition, Academic Press, 1980

[III] (with M. Reed) Methods of Modern Mathematical Physics, Vol. II: Fourier Analysis, Self Adjointness, Academic Press, 1975

[IV] The P(\phi)_2 Euclidean (Quantum) Field Theory, in Princeton Series in Physics, Princeton University Press, 1974

[V] (with M. Reed) Methods of Modern Mathematical Physics, Vol. III: Scattering Theory, Academic Press, 1979

[VI] (editor, with E. Lieb and A. Wightman) Studies in Mathematical Physics, Essays in Honor of Valentine Bargmann, Princeton University Press, 1976

[VII] (with M. Reed) Methods of Modern Mathematical Physics, Vol. IV: Analysis of Operators, Academic Press, 1977

[VIII] Trace Ideals and Their Applications, Cambridge University Press, 1979

[VIIIa] Trace Ideals and Their Applications, second edition, Mathematical Surveys and Monographs,  Vol. 120, American Mathematical Society, 2005

[IX] Functional Integration and Quantum Physics, Academic Press, 1979

[IXa]  Functional Integration and Quantum Physics, second edition, AMS Chelsea Publishing, 2005

[X] (with H. Cycon, R. Froese and W. Kirsch) Schrödinger Operators with Application to Quantum Mechanics and Global Geometry, Springer Verlag, 1987

[Xa] (with H. Cycon, R. Froese and W. Kirsch) Schrödinger Operators with Application to Quantum Mechanics and Global Geometry, corrected and extended 2nd printing, Springer Verlag,   2008

[XI] The Statistical Mechanics of Lattice Gases, Vol. I, Princeton University Press, 1993

[XII] Representations of Finite and Compact Groups, in Graduate Studies in Mathematics 10, American Mathematical Society, 1996

[XIII]  Orthogonal Polynomials on the Unit Circle, Part1: Classical Theory, AMS Colloquium Publications, American Mathematical Society, Providence, RI, 2005  [webpage]  [review

[XIV]  Orthogonal Polynomials on the Unit Circle, Part 2: Spectral Theory, AMS Colloquium Publications, American Mathematical Society, Providence, RI, 2005  [webpage]

[XV]  Szego's Theorem and Its Descendants: Spectral Theory for L2 Perturbations of Orthogonal Polynomials, M. B. Porter Lectures, Princeton University Press, Princeton, NJ, 2011  [webpage]

[XVI]  Convexity: An Analytic Viewpoint, Cambridge Tracts in Mathematics 187, Cambridge University Press, Cambridge, 2011   [webpage]

[XVII] A Comprehensive Course in Analysis, Part -1: Real Analysis, American Mathematical Society, 2015.   [webpage]  [Facebook Page] [order page]

[XVIII] A Comprehensive Course in Analysis, Part-2A: Basic Complex Analysis, American Mathematical Society, 2015.   [webpage]  [Facebook Page]  [order page]  [review]

[XIX]   A Comprehensive Course in Analysis, Part-2B: Advanced Complex Analysis, American Mathematical Society, 2015.   [webpage]   [Facebook Page[order page]

[XX]  A Comprehensive Course in Analysis, Part -3: Harmonic Analysis, American Mathematical Society, 2015.   [webpage]  [Facebook Page]  [order page]

[XXI] A Comprehensive Course in Analysis, Part-4: Operator Theory, American Mathematical Society, 2015.   [webpage]   [Facebook Page]  [order page]

### CONFERENCE PROCEEDINGS, SUMMER SCHOOL NOTES, REVIEW ARTICLES, NEWSLETTER ARTICLES

[i] Analyticity in the coupling constant and the Padé approximation, Proc. 8th Annual Eastern Theoretical Physics Conference (Syracuse 1969), Syracuse, 1970, 167-195

[ii] The anharmonic oscillator: A singular perturbation theory, Cargese Lectures in Theoretical Physics 5 (ed. D. Bessis), Gordon and Breach, 1972, 383-414

[iii] Studying spatially cutoff (\varphi^{2n})_2 Hamiltonians, Statistical Mechanics and Field Theory (ed. R.N. Sen and C. Weil), Halsted Press, New York; Israel Universities Press, Jerusalem, 1972, 197-224

[iv] Topics in functional analysis, Mathematics of Contemporary Physics (ed. R. Streater), Academic Press, 1972, 18-76

[v] Perturbation theory and coupling constant analyticity in two-dimensional field theories, Fundamental Interactions in Physics and Astronomy, Plenum, 1973, 120-136

[vi] The Glimm-Jaffe \phi-bound: A Markov proof, Constructive Quantum Field Theory (ed. G. Velo and A.S. Wightman), Springer, 1973, 125-131

[vii] Bose field theory as statistical mechanics, III. The classical Ising approximation,Constructive Quantum Field Theory, (ed. G. Velo and A.S. Wightman), Springer, 1973, 290-297

[viii] Approximation of Feynman integrals and Markov fields by spin systems, Proc. 1974 Intl. Cong. Math., 1975, 399-402

[ix] Bose quantum field theory as an Ising ferromagnet: Recent developments, Intl. Symp. on Math. Problems in Theoretical Physics (ed. H. Araki), Lecture Notes in Physics 39, Springer, 1975, 543-553

[x] An introduction to the self-adjointness and spectral analysis of Schrödinger operators, The Schrödinger Equation (ed. W. Thirring and P. Urban), Springer, 1977 (Acta Phys. Aus. Suppl. 17, Vienna, 19-42)

[xi] On the number of bound states of two-body Schrödinger operators: A review, Studies in Mathematical Physics, Essays in Honor of Valentine Bargmann (ed. E.H. Lieb, B. Simon and A.S. Wightman, Princeton University Press, Princeton, 1976, 305-326

[xii] Quantum dynamics: From automorphism to Hamiltonian, Studies in Mathematical Physics, Essays in Honor of Valentine Bargmann (ed. E.H. Lieb, B. Simon and A.S. Wightman, Princeton University Press, Princeton, 1976, 327-349

[xiii] Classical boundary conditions as a technical tool in modern mathematical physics, Adv. in Math. 30 (1978), 268-281

[xiv] New rigorous existence theorems for phase transitions in model systems, Proc. Thirteenth IUPAP Stat. Mech. Meeting (Haifa, 1977), Ann. Israel Phys. Soc. 2, Hilger, Bristol, 1978, 287-301

[xv] Resonances and complex scaling: A rigorous overview, Intl. J. Quant. Chem. 14 (1978), 529-542

[xvi] An overview of rigorous scattering theory, Atomic Scattering Theory - Mathematical and Computational Aspects (ed. J. Nuttall), Univ. of Western Ontario, Ontario, Canada, 1978, 1-24

[xvii] Identifying the classical limit of a quantum spin system, Colloq. Math. Soc. Bolyai 27 (1979), 989-1001

[xviii] Lattice systems, Encyclopedia of Statistical Sciences 4 (ed. Kotz and Johnson), Wiley, 1983, 519-522

[xix] Quantum physics and functional integration, Encyclopedia of Statistical Sciences 7 (ed. Kotz and Johnson), Wiley, 1986, 453-456

[xx] Feynman integral, McGraw-Hill Encyclopedia of Science and Technology, 5th ed., 1982, 391-392

[xxi] Schrödinger semigroups, Bull. Amer. Math. Soc. 7 (1982), 447-526

[xxii] (with V. Enss) Total cross sections in non-relativistic scattering theory, Quantum Mechanics in Mathematics, Chemistry and Physics (ed. K. Gustafson and W. Reinhardt), Plenum, 1981, 1-26

[xxiii] Large orders and summability of eigenvalue perturbation theory: A mathematical overview, Intl. J. Quant. Chem. 21 (1982), 3-25

[xxiv] Spectral analysis of multiparticle Schrödinger operators, Spectral Theory of Differential Operators (ed. I. Knowles and R.T. Lewis), North Holland, 1981, 369-370

[xxv] m-functions and the absolutely continuous spectrum of one-dimensional almost periodic Schrödinger operators, Differential Equations (ed. I. Knowles and R.T. Lewis), North Holland, 1984, 519

[xxvi] Almost periodic Schrödinger operators: A review, Adv. Appl. Math. 3 (1982), 463-490

[xxvii] Fifteen problems in mathematical physics, Oberwolfach Anniversary Volume, 1984, 423-454

[xxviii] Boundedness of continuum eigenfunctions and their relation to spectral problems, Linear and Complex Analysis Problem Book: 199 Research Problems (ed. V. Havin, S. Hruscev, and N. Nikol'skii), Lecture Notes in Mathematics 1043, Springer, 1984, 113-115

[xxix] (with E.B. Davies) Ultracontractive semigroups and some problems in analysis, Aspects of Mathematics and its Applications (ed. J. Barroso), Elsevier, 1986

[xxx] (with B. Souillard) Franco-American meeting on the mathematics of random and almost periodic potentials, J. Statist. Phys. 36 (1984), 273-288

[xxxi] Some aspects of the theory of Schrödinger operators, Schrödinger Operators, Como 1984 (ed. S. Graffi), Lecture Notes in Mathematics 1159, Springer, 1985, 177-203

[xxxii] Lifshitz tails for the Anderson model, J. Statist. Phys. 38 (1985), 65-76

[xxxiii] Regularity of the density of states for stochastic Jacobi matrices: A review, IMA Conf. Proc., Random Media 7 (1987), 245-266

[xxxiv] Schrödinger operators with random and almost periodic potentials, Recent Developments in Mathematical Physics (ed. H. Mitter and L. Pittner), Springer, New York, 1987, 100-101.

[xxxv] (with E.B. Davies and L. Gross) Hypercontractivity: A bibliographic review, Proc. Hoegh Krohn Memorial Conference, Ideas and Methods in Quantum and Statistical Physics (Oslo, 1988), 370-389, Cambridge Univ. Press, Cambridge, 1992.

[xxxvi] Fifty years of eigenvalue perturbation theory, Bull. Amer. Math. Soc. 24 (1991), 303-319

[xxxvii] The Scott correction and the quasi-classical limit, Asterisque 210 (1992), 295-302

[xxxviii] Spectral analysis of rank one perturbations and applications, Proc. Mathematical Quantum Theory, II: Schrödinger Operators (eds. J. Feldman, R. Froese and L. Rosen) CRM Proc. Lecture Notes 8 (1995), 109-149

[xxxix] Schrödinger operators in the twentieth century, J. Math. Phys. 41 (2000), 3523-3555

[xl] Schrödinger operators in the twenty-first century, Mathematical Physics 2000 (eds. A. Fokas, A. Grigoryan, T. Kibble and B. Zegarlinski), Imperial College Press, London, 283-288

[xli] (with H. Cordes, A. Jensen, S. T. Kuroda, G. Ponce and M. Taylor) Tosio Kato (1917-1999), Notices A.M.S  47 (2000), 650-657

[xlii] Sturm oscillation and comparison theorems, Sturm-Liouville Theory: Past and Present (eds. W. Amrein, A. Hinz and D. Pearson), Birkhauser, Basel, 2005, 29-43

[xliii] Analogs of the m-function in the theory of orthogonal polynomials on the unit circle, J. Comp. Appl. Math. 171 (2004), 411-424

[xliv] The sharp form of the strong Szegö theorem, Geometry, spectral theory, groups, and dynamics, Contemp. Math. 387 (2005), 253-275, Amer. Math. Soc., Providence, RI

[xlv]  Ed Nelson's work in quantum theory, Diffusion, Quantum Theory, and Radically Elementary Mathematics (ed. W. G. Faris), Mathematical Notes 47, Princeton University Press, 2006, 75-93. This article has been reprinted as part of an obituary for Ed. Nelson in the IAMP Bulletin for April, 2015

[xlvi] OPUC on one foot, Bull. Amer. Math. Soc. 42 (2005), 431-460

[xlvii] CMV matrices: Five years after, J. Comput. Appl. Math. 208 (2007), 120-154

[xlviii] Orthogonal polynomials with exponentially decaying recursion coefficients, Probability and Mathematical Physics (eds. D. Dawson, V. Jaksic and B. Vainberg), CRM Proc. and Lecture Notes 42 (2007), 453-463.

[xlix] Fine structure of the zeros of orthogonal polynomials: A review, Difference Equations, Special Functions and Orthogonal Polynomials (eds. S. Elaydi et al.), World Sci. Publ., Singapore, 2007, 636-653.

[l]  (with J. Christiansen and M. Zinchenko) Finite gap Jacobi matrices: An announcement, J. Comp. Applied Math. 233 (2009), 652-662

[li]  (with D. Damanik and A. Pushnitski) The analytic theory of matrix orthogonal polynomials, Surveys in Approximation Theory 4 (2008), 1-85.

[lii] The Christoffel-Darboux kernel, in "Perspectives in PDE, Harmonic Analysis and Applications," a volume in honor of V.G. Maz'ya's 70th birthday, Proceedings of Symposia in Pure Mathematics 79 (2008), 295-335

[liii] A celebration of Jürg and Tom, J. Statist. Phys. 134 (2009), 809-812 (special issue in honor of  the 60th birthday of Jürg Fröhlich and Tom Spencer)  WARNING: Video is over 1.3 GB!

[liv] Fine structure of the zeros of orthogonal polynomials: A progress report, in "Recent Trends in Orthogonal Polynomials and Approximation Theory," a volume in honor of Guillermo Lopez's 60th birthday,  Contemporary Math. 507 (2010), 241-254.

[lv] Spectral theory of orthogonal polynomials, Proc. ICMP 2012, Aalborg, World Scientific, Singapore, 2014, 217-228

[lvi]  (with J. Christiansen and M. Zinchenko) Finite gap Jacobi matrices: A review, in Spectral Analysis, Differential Equations and Mathematical Physics, A Festschrift for Fritz Gesztesy on the Occasion of his 60th Birthday, ed. H. Holden, B. Simon and G. Teschl, AMS, Proceedings of Symposia in Pure Mathematics 87 (2013),  87-103

[lvii] Mathematical physics at Princeton in the 1970s, IAMP News Bulletin, July 2012

[lviii] (with A. Jaffe) Obituary: Arthur Strong Wightman (1922-2013), IAMP News Bulletin, January 2013

[lix] (B. Simon was coordinating editor; contributions by  J. Frohlich, F. Guerra, K. Hepp, A. Jaffe, C. Nappi, E. Nelson, D. Ruelle, B. Simon, R. Streater, F. Strocchi and G. Velo), In Memory of Arthur Strong  Wightman, Notices A.M.S  62 (2015), 249-257

[lx] Spectral Theory Sum Rules, Meromorphic Herglotz Functions and Large Deviations, Notices A.M.S. 64 (2017) 9-10, blurb for JMM plenary talk, Atlanta, Jan, 2017.

[lxi] Tosio Kato's Work on Non{Relativistic Quantum Mechanics: part 1, Bulletin of Mathematical Sciences, 8 (2018), 121-232.

[lxii].Tosio Kato's Work on Non{Relativistic Quantum Mechanics: part 2, Bulletin of Mathematical Sciences, to appear.

[lxiii]  Tosio Kato's Work on Non--Relativistic Quantum Mechanics: An Outline, to appear in Proc. Kato Centenial Conference.

[lxiv] Tosio Kato's Work on Non{Relativistic Quantum Mechanics: A Brief Report, IAMP News Bulletin, January, 2018.

[lxv] Tosio Kato's Work on Non{Relativistic Quantum Mechanics: A Brief Report, to appear in Analysis and Operator Theory In Honor of Tosio Katos 100 th Birthday, a volume edited by Th. M. Rassias and V. Zagrebnov to be published by Springer..

### TALKS (may only be posted temporarily)

1.  Talk given at IWOPA '08 (Madrid, September 2008 in honor of Bill Lopez)  [pdf] [video]

2. Talk given at Newton Institute (December 2008)  [video]

3.  Tales of our Forefathers talk [pdf] [video] (Video Courtesy Issac Newton Institute) WARNING: Video is over 1.3 GB!  Another version on YouTube.

4.  More Tales of our Forefathers talk [pdf] [video] (Video Courtesy Issac Newton Institute) WARNING: Video is over 2.2 GB!

5.  Videos and Slides of 8 lectures on Spectral Theory of Orthogonal Polynomials givren at Issac Newton Institute are available

6. Talk given at Celebrating the work of Prof. Edward Nelson (1932-2014), Princeton Math Colloquium, April 22, 2015. [pdf]

7.  Acceptance Talk at Bolyai Prize Ceremony (on "OPUC and me") [pdf]

8.  Talks on Large Deviations and Sum Rules for Orthogonal Polynomials at 14th Latin American Congress of Probability (CLAPEM XIV), Dec. 5-6, 2016, San Jose, Costa Rica:  Lectures one, two, three, four

9. Talk on Periodic Trees, 2019 [pdf]