provides a pdf of the article for your personal,
non-commercial use and should not be reposted. 
will take you to the journal site and require you
or your institution to have a subscription.| Return to Home Page | Books | Proceedings |
| Coauthors | Bibliography | Talks |
provides a pdf of the article for your personal,
non-commercial use and should not be reposted. will take you to the journal site and require you
or your institution to have a subscription.[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 (φ4)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. Høegh-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 (φ2n)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(φ)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(φ)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(φ)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(φ)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(φ)2 quantum field theory, Phys.
Lett. 44B (1973), 102-104
[33] (with F. Guerra and L. Rosen)
The P(φ)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(φ)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(φ)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 (φ4)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 (φ4)2 field theory as a
classical Ising model, Commun.
Math. Phys. 33 (1973),
145-164
[48] Correlation inequalities and the mass gap in P(φ)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(φ)2,
Bull. Amer.
Math. Soc. 80 (1974), 1205-1209
[50] (with F. Guerra and L. Rosen)
Correlation inequalities and the mass gap in P(φ)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(φ)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 Yukawa2 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
Yukawa2 and (φ4)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(φ)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 Ip 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, quarternions, 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
[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(φ)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]
[XXII] Loewner's Theorem on Matrix Monotone Functions, Grundlehren der mathematischen Wissenschaften 354, 2019 [order page]
[XXIII] Phase Transitions in the Theory of Lattice Gases, Cambridge University Press, 2024 (expected)
[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 (φ2n)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 φ-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, 9 (2019), (195005)1-105.
[lxiii] Tosio Kato's Work on Non--Relativistic Quantum Mechanics: An Outline, to appear in Proc. Kato Centenial Conference.
[lxv] Tosio Kato's Work on Non--Relativistic Quantum Mechanics: A Brief Report, Analysis and Operator Theory In Honor of Tosio Kato's 100th Birthday, a volume edited by Th. M. Rassias and V. Zagrebnov, Springer, 2019; pp 353-378...
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]