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The mathematical theory of resonances whose widths are exponentially small, II, J.
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Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet
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Spectral properties of the Neumann Laplacian of horns, Geom. Funct. Anal. 2
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Asymptotic series for the ground state energy of Schrödinger operators, J. Funct.
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Spectral properties of random Schrödinger operators with unbounded potentials, Commun.
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Operators with singular continuous spectrum, V. Sparse potentials, Proc. Amer. Math.
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[248] Operators with singular continuous spectrum, VII. Examples with borderline time
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Operators with singular continuous spectrum, IV. Hausdorff dimensions, rank one
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[253] Bounded eigenfunctions and absolutely continuous spectra for one-dimensional
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Weakly coupled bound states in quantum waveguides, Proc. Amer. Math. Soc. 125
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Duality and singular continuous spectrum in the almost Mathieu equation, Acta Math.
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[261] (with F.
Gesztesy) m-functions and inverse spectral analysis for finite and semi-infinite
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Connectedness of the isospectral manifold for one-dimensional half-line
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Necessary and sufficient conditions in the spectral theory of Jacobi matrices
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Schrödinger operators with few bound states, Comm. Math. Phys. 258 (2005), 741-750
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Higher-order Szego theorems with two singular points, J. Approx.
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Jost functions and Jost solutions for Jacobi matrices, I. A necessary and
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Jost functions and Jost solutions for Jacobi matrices, II. Decay and
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[305] Meromorphic Jost functions and asymptotic expansion for Jacobi
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Sum rules and spectral measures of Schrödinger operators with L2
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Perturbations of orthogonal polynomials with periodic recursion coefficients, Annals of Math.
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T. Weidl)
Eigenvalue bounds for perturbations of Schrödinger operators and Jacobi matrices
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[314] (with
F. Gesztesy and
A. Pushnitski) On the Koplienko
spectral shift function, I. Basics, Zh. Mat. Fiz. Anal. Geom. 4
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[315] (with D. Hundertmark) Eigenvalue
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[317] Equilibrium measures and capacities in spectral theory, Inverse Problems and Imaging 1
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[318] Weak convergence of CD kernels and applications,
Duke Math. J. 146 (2009), 305-330
[319] Regularity and the Cesàro–Nevai class, J.
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[320] (with Y. Kreimer and Y. Last) Monotone Jacobi parameters and
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M. Zinchenko) Finite gap Jacobi matrices, I.
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[325] (with A. Poltoratski and
M. Zinchenko) The Hilbert transform of a
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M. Zinchenko) Finite gap Jacobi matrices, II.
The Szegö class, Constr. Approx. 33 (2011), 365-403
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Natural boundaries and spectral theory, Advances in Mathematics 226
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Critical Lieb-Thirring bounds in gaps and the generalized Nevai conjecture for
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[xxviii] Boundedness of continuum eigenfunctions and their relation to spectral
problems, Linear and Complex Analysis Problem Book: 199 Research
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N. Nikol'skii), Lecture Notes in Mathematics 1043, Springer, 1984,
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[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] Sturm oscillation and comparison theorems, Sturm-Liouville Theory:
Past and Present (eds. W. Amrein, A. Hinz and D. Pearson), Birkhauser,
Basel, 2005, 29-43
[xlii] Analogs of the m-function in the theory of orthogonal
polynomials on the unit circle, J. Comp. Appl. Math. 171
(2004), 411-424
[xliii] 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
[xliv] 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.
[xlv] OPUC on one foot, Bull. Amer. Math.
Soc. 42 (2005), 431-460
[xlvi] CMV matrices: Five years after, J. Comput. Appl.
Math. 208 (2007), 120-154
[xlvii] 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.
[xlviii] 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.
[xlix] (with J.
Christiansen and M. Zinchenko)
Finite gap Jacobi matrices: An announcement, J. Comp. Applied Math.
233 (2009), 652-662
[l] (with D. Damanik
and A. Pushnitski) The analytic
theory of matrix orthogonal polynomials, Surveys in Approximation
Theory 4 (2008), 1-85.
[li] 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
[lii] 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)
[liii] 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.
1. Talk given at IWOPA '08 (Madrid, September 2008 in honor of Bill Lopez) [pdf] [video]
2. Talk given at Newton Institute (December 2008) [pdf] [video]