Barry Simon
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American mathematician
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Mathematics
Barry Simon's Degrees
- PhD Mathematics Princeton University
Why Is Barry Simon Influential?
(Suggest an Edit or Addition)According to Wikipedia, Barry Martin Simon is an American mathematical physicist and was the IBM professor of Mathematics and Theoretical Physics at Caltech, known for his prolific contributions in spectral theory, functional analysis, and nonrelativistic quantum mechanics , including the connections to atomic and molecular physics. He has authored more than 400 publications on mathematics and physics.
Barry Simon's Published Works
Published Works
- Trace ideals and their applications (1979) (2248)
- Methods of Modern Mathematical Physics. 2. Fourier Analysis, Self-adjointness (1975) (1852)
- Schrodinger Operators: With Application to Quantum Mechanics and Global Geometry (1987) (1463)
- Functional integration and quantum physics (1979) (1400)
- Holonomy, the Quantum Adiabatic Theorem, and Berry's Phase (1983) (1298)
- Methods of modern mathematical physics. III. Scattering theory (1979) (1242)
- The P(φ)[2] Euclidean (quantum) field theory (1974) (990)
- Schrödinger Semigroups (2007) (645)
- Analysis of Operators (1978) (628)
- Fourier Analysis, Self-Adjointness (1975) (593)
- The Thomas-Fermi theory of atoms, molecules and solids (1977) (589)
- The statistical mechanics of lattice gases (1993) (555)
- Coupling constant analyticity for the anharmonic oscillator (1970) (512)
- Schrödinger operators with magnetic fields. I. general interactions (1978) (499)
- Resonances in n-Body Quantum Systems With Dilatation Analytic Potentials and the Foundations of Time-Dependent Perturbation Theory (1973) (491)
- Quantum Mechanics for Hamiltonians Defined as Quadratic Forms (1971) (486)
- Orthogonal Polynomials on the Unit Circle (2004) (486)
- The bound state of weakly coupled Schrödinger operators in one and two dimensions (1976) (482)
- Orthogonal polynomials on the unit circle. Part 1 (2005) (477)
- The Classical Moment Problem as a Self-Adjoint Finite Difference Operator (1998) (468)
- Infrared bounds, phase transitions and continuous symmetry breaking (1976) (459)
- Schrödinger operators with magnetic fields (1981) (446)
- Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians (1984) (432)
- The Hartree-Fock theory for Coulomb systems (1977) (407)
- Representations of finite and compact groups (1995) (405)
- Szegő's Theorem and Its Descendants: Spectral Theory for L 2 Perturbations of Orthogonal Polynomials (2010) (400)
- Brownian motion and harnack inequality for Schrödinger operators (1982) (388)
- The definition of molecular resonance curves by the method of exterior complex scaling (1979) (376)
- Singular continuous spectrum under rank one perturbations and localization for random hamiltonians (1986) (367)
- Homotopy and Quantization in Condensed Matter Physics (1983) (366)
- Quadratic form techniques and the Balslev-Combes theorem (1972) (351)
- Spectral analysis of rank one perturbations and applications (1995) (341)
- The P(φ) 2 Euclidean Quantum Field Theory as Classical Statistical Mechanics (1975) (306)
- Almost periodic Schrödinger operators II. The integrated density of states (1983) (298)
- Semiclassical analysis of low lying eigenvalues, II. Tunneling* (1984) (285)
- Operators with singular continuous spectrum, IV. Hausdorff dimensions, rank one perturbations, and localization (1996) (282)
- Almost periodic Schrödinger operators: A Review (1982) (276)
- Relativistic Schrödinger operators: Asymptotic behavior of the eigenfunctions (1990) (270)
- Notes on infinite determinants of Hilbert space operators (1977) (270)
- Phase transitions in quantum spin systems with isotropic and nonisotropic interactions (1978) (270)
- Sum rules for Jacobi matrices and their applications to spectral theory (2001) (262)
- A canonical decomposition for quadratic forms with applications to monotone convergence theorems (1978) (261)
- Spectral analysis of N-body Schrodinger operators * (1981) (261)
- Semiclassical analysis of low lying eigenvalues. I. Non-degenerate minima : asymptotic expansions (1983) (259)
- Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schrödinger operators (1999) (254)
- The Index of a Pair of Projections (1994) (252)
- Inverse spectral analysis with partial information on the potential, II. The case of discrete spectrum (1999) (243)
- Separation of center of mass in homogeneous magnetic fields (1978) (242)
- Hypercontractive semigroups and two dimensional self-coupled Bose fields (1972) (238)
- Almost periodic Schrödinger operators (1981) (219)
- Borel summability: Application to the anharmonic oscillator (1970) (218)
- The (φ4)2 field theory as a classical Ising model (1973) (216)
- The Analytic Theory of Matrix Orthogonal Polynomials (2007) (211)
- Weakly coupled bound states in quantum waveguides (1997) (194)
- Modified Prüfer and EFGP Transforms and the Spectral Analysis of One-Dimensional Schrödinger Operators (1998) (190)
- Charge deficiency, charge transport and comparison of dimensions (1998) (187)
- Methods of Mathematical Physics (1980) (186)
- Coupling constant thresholds in nonrelativistic quantum mechanics. I. Short-range two-body case (1980) (185)
- Pade approximants and the anharmonic oscillator (1969) (184)
- Phase Transitions and Reflection Positivity . I . General Theory and Long Range Lattice Models (1978) (184)
- Cantor spectrum for the almost Mathieu equation (1982) (184)
- Correlation inequalities and the decay of correlations in ferromagnets (1980) (183)
- Classical and Multilinear Harmonic Analysis (2011) (177)
- Operators with singular continuous spectrum (1995) (176)
- Some quantum operators with discrete spectrum but classically continuous spectrum (1983) (173)
- Singular continuous spectrum for palindromic Schrödinger operators (1995) (172)
- CMV matrices: Five years after (2006) (165)
- Kotani theory for one dimensional stochastic Jacobi matrices (1983) (164)
- Phase transitions and reflection positivity. I. General theory and long range lattice models (1978) (164)
- Almost periodic Schrödinger operators (1983) (159)
- Resonances and complex scaling: a rigorous overview (1978) (159)
- Schrödinger operators in the twentieth century (2000) (158)
- A new approach to inverse spectral theory, I. Fundamental formalism (1999) (156)
- Operator Theory: A Comprehensive Course in Analysis, Part 4 (2015) (156)
- The classical limit of quantum partition functions (1980) (152)
- Large orders and summability of eigenvalue perturbation theory: A mathematical overview (1982) (149)
- Thomas-Fermi Theory Revisited (1973) (148)
- Distributions and Their Hermite Expansions (1971) (140)
- Resonances in One Dimension and Fredholm Determinants (2000) (139)
- Operators with Singular Continuous Spectrum: I. General Operators (1995) (138)
- A new approach to inverse spectral theory, II. General real potentials and the connection to the spectral measure (1998) (136)
- Scattering theory for systems with different spatial asymptotics on the left and right (1978) (136)
- Singular continuous spectrum for a class of almost periodic Jacobi matrices (1982) (132)
- Phase space analysis of simple scattering systems: extensions of some work of Enss (1979) (132)
- Comparison theorems for the gap of Schrödinger òperators (1987) (131)
- Topics in Ergodic Theory (1994) (130)
- Operators with singular continuous spectrum: III. Almost periodic Schrödinger operators (1994) (128)
- Subharmonicity of the Lyaponov index (1983) (126)
- Convexity: An Analytic Viewpoint (2011) (126)
- m-Functions and inverse spectral analysis for finite and semi-infinite Jacobi matrices (1997) (123)
- On positive eigenvalues of one‐body schrödinger operators (1969) (119)
- Duality and singular continuous spectrum in the almost Mathieu equation (1997) (118)
- Kato's inequality and the comparison of semigroups☆ (1979) (116)
- The Christoffel-Darboux Kernel (2008) (116)
- Bounded eigenfunctions and absolutely continuous spectra for one-dimensional Schrödinger operators (1996) (116)
- The essential spectrum of Neumann Laplacians on some bounded singular domains (1991) (116)
- Lifschitz tails for the Anderson model (1985) (114)
- Log hölder continuity of the integrated density of states for stochastic Jacobi matrices (1983) (114)
- Behavior of molecular potential energy curves for large nuclear separations (1980) (113)
- The xi function (1996) (111)
- SCHRÖDINGER OPERATORS IN THE TWENTY-FIRST CENTURY (2000) (111)
- Perturbations of orthogonal polynomials with periodic recursion coefficients (2007) (110)
- Inverse spectral analysis with partial information on the potential. III. Updating boundary conditions (1997) (109)
- Stark Effect Revisited (1978) (107)
- Pointwise bounds on eigenfunctions and wave packets inN-body quantum systems IV (1978) (106)
- From power pure point to continuous spectrum in disordered systems (1985) (103)
- Large time behavior of the Lp norm of Schrödinger semigroups (1981) (103)
- Geometric methods in multiparticle quantum systems (1977) (103)
- On Local Borg–Marchenko Uniqueness Results (1999) (102)
- EQUILIBRIUM MEASURES AND CAPACITIES IN SPECTRAL THEORY (2007) (100)
- The Absolutely Continuous Spectrum in One Dimension (1983) (100)
- OPUC on one foot (2005) (95)
- Rank One Perturbations at Infinite Coupling (1995) (94)
- Pointwise bounds on eigenfunctions and wave packets in $N$-body quantum systems. V. Lower bounds and path integrals (1981) (94)
- Some Schrödinger operators with dense point spectrum (1997) (94)
- Harmonic analysis on SL(2,R) and smoothness of the density of states in the one-dimensional Anderson model (1985) (93)
- Uniqueness theorems in inverse spectral theory for one-dimensional Schrödinger operators (1996) (92)
- The mathematical theory of resonances whose widths are exponentially small (1980) (92)
- On the measure of the spectrum for the almost Mathieu operator (1991) (91)
- Bounds in the Yukawa2 quantum field theory: Upper bound on the pressure, Hamiltonian bound and linear lower bound (1975) (90)
- Trace class perturbations and the absence of absolutely continuous spectra (1989) (90)
- Monotonicity of the electronic contribution to the Born-Oppenheimer energy (1978) (90)
- Nonclassical eigenvalue asymptotics (1983) (88)
- The bound states of weakly coupled long-range one-dimensional quantum hamiltonians (1977) (88)
- Stochastic Schrödinger operators and Jacobi matrices on the strip (1988) (86)
- The Essential Spectrum of Schrödinger, Jacobi, and CMV Operators (2005) (86)
- Brownian motion, Lp properties of Schrödinger operators and the localization of binding ☆ (1980) (84)
- Zeros of the Wronskian and renormalized oscillation theory (1996) (84)
- Essential self-adjointness of Schrödinger operators with positive potentials (1973) (82)
- Localization in general one-dimensional random systems (1987) (82)
- Two extensions of Lubinsky’s universality theorem (2008) (81)
- From power-localized to extended states in a class of one-dimensional disordered systems (1984) (81)
- Schrödinger operators with an electric field and random or deterministic potentials (1983) (81)
- Texts and Monographs in Physics (1987) (81)
- Some jacobi matrices with decaying potential and dense point spectrum (1982) (79)
- Nelson's symmetry and all that in the Yukawa2 and (φ4)3 field theories☆ (1976) (78)
- Szego's Theorem and Its Descendants: Spectral Theory for L2 Perturbations of Orthogonal Polynomials (M. B. Porter Lectures) (2010) (77)
- Commutation methods applied to the mKdV-equation (1991) (77)
- Witten index, axial anomaly, and Krein's spectral shift function in supersymmetric quantum mechanics (1987) (76)
- Operators with singular continuous spectrum: II. Rank one operators (1994) (76)
- Schrödinger operators with singular magnetic vector potentials (1973) (75)
- INVERSE SPECTRAL ANALYSIS WITH PARTIAL INFORMATION ON THE POTENTIAL, I. THE CASE OF AN A.C. COMPONENT IN THE SPECTRUM (1997) (75)
- Lieb-Thirring Inequalities for Jacobi Matrices (2001) (73)
- On the determination of a potential from three spectra (1999) (73)
- Almost periodic Schrödinger operators IV. The maryland model (1985) (73)
- Methods of Mathematical Physics, V. I: Functional Analysis. (1973) (72)
- Semiclassical analysis of low lying eigenvalues. IV. The flea on the elephant (1985) (72)
- On the decoupling of finite singularities from the question of asymptotic completeness in two body quantum systems (1976) (70)
- Basic Complex Analysis: A Comprehensive Course in Analysis, Part 2A (2015) (69)
- Wave operators for classical particle scattering (1971) (68)
- Rank One Perturbations with Infinitesimal Coupling (1995) (68)
- On the absorption of eigenvalues by continuous spectrum in regular perturbation problems (1977) (67)
- Transient and Recurrent Spectrum (1981) (67)
- Unique continuation for Schrodinger operators with unbounded potentials (1980) (65)
- FINE STRUCTURE OF THE ZEROS OF ORTHOGONAL POLYNOMIALS, I. A TALE OF TWO PICTURES (2004) (65)
- Absence of ballistic motion (1990) (62)
- The asymptotics of the gap in the Mathieu equation (1981) (62)
- Lifshitz tails for periodic plus random potentials (1986) (62)
- Dilation analyticity in constant electric field (1981) (62)
- Cyclic Vectors in the Anderson Model (1994) (61)
- Real Analysis: A Comprehensive Course in Analysis, Part 1 (2015) (61)
- Essential self-adjointness of Schrödinger operators with singular potentials (1973) (61)
- Best constants in some operator smoothness estimates (1992) (61)
- Operators with singular continuous spectrum, V. Sparse potentials (1996) (60)
- Weak convergence of CD kernels and applications (2007) (60)
- Fifty years of eigenvalue perturbation theory (1991) (59)
- Invariant domains for the time-dependent Schrödinger equation☆ (1978) (59)
- Nelson's symmetry and the infinite volume behavior of the vacuum inP(φ)2 (1972) (59)
- Functional Integration and Quantum Physics: Second Edition (2004) (58)
- Sturm Oscillation and Comparison Theorems (2003) (58)
- Spectral averaging and the Krein spectral shift (1998) (58)
- A new approach to inverse spectral theory (2016) (57)
- Phase Transitions and Reflection Positivity . II . Lattice Systems with Short-Range and Coulomb Interactions (1979) (56)
- Hamiltonians defined as quadratic forms (1971) (56)
- Phase transitions and reflection positivity. II. Lattice systems with short-range and Coulomb interactions (1980) (55)
- Jost functions and Jost solutions for Jacobi matrices, I. A necessary and sufficient condition for Szegő asymptotics (2005) (55)
- Universal Diamagnetism of Spinless Bose Systems (1976) (55)
- Rigorous entropy-energy arguments (1981) (54)
- The calculation of molecular resonances by complex scaling (1981) (53)
- Phase Transitions in the Quantum Heisenberg Model (1976) (53)
- A remark on Dobrushin's uniqueness theorem (1979) (53)
- Analysis with weak trace ideals and the number of bound states of Schrödinger operators (1976) (53)
- A short proof of Zheludev's theorem (1993) (52)
- A diamagnetic inequality for semigroup differences (2004) (52)
- Lp spectral theory of Kleinian groups (1988) (52)
- Analytic properties of band functions (1978) (52)
- OPERATORS WITH SINGULAR CONTINUOUS SPECTRUM : II (2002) (52)
- Quadratic forms and Klauder's phenomenon: A remark on very singular perturbations (1973) (51)
- On solutions to the Hartree‐Fock problem for atoms and molecules (1974) (51)
- Instantons, double wells and large deviations (1983) (51)
- Lp norms of non-critical Schrödinger semigroups (1991) (51)
- Fine structure of the zeros of orthogonal polynomials IV: A priori bounds and clock behavior (2006) (51)
- Sum Rules and the Szegő Condition for Orthogonal Polynomials on the Real Line (2002) (50)
- Semiclassical analysis of low lying elgenvalues. III. Width of the ground state band in strongly coupled solids (1984) (50)
- Corrections to the classical behavior of the number of bound states of Schrödinger operators (1988) (50)
- Pointwise bounds on eigenfunctions and wave packets inN-body quantum systems (1978) (49)
- Asymptotic Neutrality of Large- Z Ions (1984) (48)
- Trapping and cascading of eigenvalues in the large coupling limit (1988) (47)
- Harmonic Analysis: A Comprehensive Course in Analysis, Part 3 (2015) (46)
- On the Toda and Kac-van Moerbeke systems (1993) (46)
- Rank one perturbations and the zeros of paraorthogonal polynomials on the unit circle (2006) (46)
- The Statistical Mechanics of Lattice Gases, Volume I (2014) (46)
- Variational Estimates for Discrete Schrödinger Operators with Potentials of Indefinite Sign (2002) (46)
- Quantum Magnetic Hamiltonians with Remarkable Spectral Properties (1980) (46)
- Spectral deformations of one-dimensional Schrödinger operators (1996) (46)
- A multiparticle Coulomb system with bound state at threshold (1983) (46)
- HIGHER ORDER TRACE RELATIONS FOR SCHRÖDINGER OPERATORS (1995) (46)
- Almost Periodic Hill's Equation and the Rings of Saturn (1981) (46)
- Universal lower bounds on eigenvalue splittings for one dimensional Schrödinger operators (1985) (45)
- Trace formulae and inverse spectral theory for Schr (1993) (45)
- Spectrum and continuum eigenfunctions of Schrödinger operators (1981) (45)
- Approximate neutrality of large-Z ions (1988) (45)
- Eigenvalue bounds for Schrödinger operators with complex potentials. II (2017) (45)
- Eigenvalue asymptotics of the Neumann Laplacian of regions and manifolds with cusps (1992) (44)
- Some remarkable examples in eigenvalue perturbation theory (1978) (44)
- Lower semicontinuhy of positive quadratic forms (1978) (44)
- On the measure of the spectrum for the almost Mathieu operator (1990) (44)
- Jost functions and Jost solutions for Jacobi matrices, II. Decay and analyticity (2005) (44)
- Singular continuous spectrum is generic (1994) (44)
- Topological invariance of the Witten index (1988) (43)
- Higher-order Szego theorems with two singular points (2004) (43)
- Finite Gap Jacobi Matrices, I. The Isospectral Torus (2008) (42)
- A time-dependent approach to the completeness of multiparticle quantum systems (1977) (42)
- The Zeeman effect revisited (1977) (41)
- Spectral properties of Neumann Laplacian of horns (1992) (41)
- On a theorem of Deift and Hempel (1988) (41)
- Correlation inequalities and the mass gap inP(φ)2 (1973) (41)
- Sum rules and spectral measures of Schrödinger operators with L^2 potentials (2006) (41)
- Phase Transitions and Continuous Symmetry Breaking (1976) (40)
- On the Koplienko Spectral Shift Function. I. Basics (2007) (40)
- Loewner's Theorem on Monotone Matrix Functions (2019) (40)
- Pointwise bounds on eigenfunctions and wave packets in $N$-body quantum systems. III (1975) (40)
- Absence of positive eigenvalues in a class of multiparticle quantum systems (1974) (39)
- Bulk Universality and Clock Spacing of Zeros for Ergodic Jacobi Matrices with A.C. Spectrum (2008) (37)
- Schrödinger Operators with Purely Discrete Spectrum (2008) (37)
- Eigenvalue Bounds for Perturbations of Schrödinger Operators and Jacobi Matrices With Regular Ground States (2007) (36)
- On the genericity of nonvanishing instability intervals in Hills equation (1976) (36)
- Bulk universality and clock spacing of zeros for ergodic Jacobi matrices with absolutely continuous spectrum (2010) (36)
- Fine structure of the zeros of orthogonal polynomials, II. OPUC with competing exponential decay (2004) (36)
- A Trace Formula for Multidimensional Schrödinger Operators (1996) (36)
- Ordinary differential equations in the complex domain (2015) (36)
- Absence of absolutely continuous spectrum for some one dimensional random but deterministic Schrödinger operators (1985) (35)
- Effective Perturbation Methods for One-Dimensional Schrödinger Operators (1999) (35)
- Operators with singular continuous spectrum, VII. Examples with borderline time decay (1996) (35)
- Studies in mathematical physics : essays in honor of Valentine Bargmann (2015) (35)
- Analogs of the m -function in the theory of orthogonal polynomials on the unit circle (2003) (35)
- An optimalLp-bound on the Krein spectral shift function (2002) (35)
- Pointwise bounds on eigenfunctions and wave packets in $N$-body quantum systems. II (1974) (34)
- Existence of the scattering matrix for the linearized Boltzmann equation (1975) (34)
- Equality of the Spectral and Dynamical Definitions of Reflection (2009) (34)
- Stability of Spectral Types for Sturm-Liouville Operators (1994) (34)
- Jost functions and Jost solutions for Jacobi matrices, III. Asymptotic series for decay and meromorphicity (2005) (34)
- Absolute summability of the trace relation for certain Schrödinger operators (1995) (34)
- Constructing Solutions of the mKdV-Equation (1990) (33)
- The vacuum energy forP(ø)2: Infinite volume limit and coupling constant dependence (1973) (33)
- Operators with singular continuous spectrum, VI. Graph Laplacians and Laplace-Beltrami operators (1996) (32)
- Degenerate and non-degenerate ground states for Schrödinger operators (1975) (32)
- The Neumann Laplacian of a jelly roll (1992) (32)
- On finite mass renormalizations in the two‐dimensional Yukawa model (1975) (32)
- Classical boundary conditions as a technical tool in modern mathematical physics (1978) (32)
- Local Ward identities and the decay of correlations in ferromagnets (1980) (32)
- Strongly bound states of hydrogen in intense magnetic field (1979) (32)
- A remark on Nelson’s best hypercontractive estimates (1976) (31)
- L^p Norms of the Borel Transform and the Decomposition of Measures (1995) (31)
- INFINITUDE OR FINITENESS OF THE NUMBER OF BOUND STATES OF AN N-BODY QUANTUM SYSTEM. I. (1970) (31)
- Fine structure of the zeros of orthogonal polynomials III: Periodic recursion coefficients (2004) (31)
- Eigenvalue estimates for non-normal matrices and the zeros of random orthogonal polynomials on the unit circle (2006) (31)
- Finite Gap Jacobi Matrices, II. The Szegő Class (2009) (31)
- Fine Structure of the Zeros of Orthogonal Polynomials: A Review (2007) (31)
- Tensor products of closed operators on Banach spaces (1973) (30)
- Formation of negative ions in magnetic fields (1977) (29)
- Bender-Wu Formula and the Stark Effect in Hydrogen (1979) (29)
- Zeros of OPUC and long time asymptotics of Schur and related flows (2006) (29)
- Orthogonal polynomials on the unit circle: New results (2004) (29)
- Localization in general one dimensional random systems, I. Jacobi matrices (1985) (28)
- Relative rearrangement on a finite measure space: application to the regularity of weighted monotone rearrangement (Part I) (1993) (28)
- Borel Summability of the Ground-State Energy in Spatially Cutoff (ϕ^4)_2 (1970) (28)
- Ratio asymptotics and weak asymptotic measures for orthogonal polynomials on the real line (2004) (28)
- Zeros of orthogonal polynomials on the real line (2002) (27)
- The scattering of classical waves from inhomogeneous media (1977) (27)
- Large time behavior of the heat kernel: on a theorem of Chavel and Karp (1993) (27)
- Asymptotics of Chebyshev polynomials, I: subsets of $${\mathbb {R}}$$R (2015) (27)
- The Nevai Condition (2008) (27)
- Correlation inequalities and the mass gap inP (φ)2 (1973) (26)
- Ergodic semigroups of positivity preserving self-adjoint operators (1973) (26)
- A new approach to inverse spectral theory, III. Short-range potentials (2000) (25)
- L1-properties of intrinsic Schrödinger semigroups (1986) (25)
- Binding of Schrödinger particles through conspiracy of potential wells (1979) (25)
- Stability of singular spectral types under decaying perturbations (2001) (25)
- The Weyl Transform and L^p Functions on Phase Space (1992) (25)
- Multiparticle Quantum Scattering with Applications to Nuclear Atomic and Molecular Physics (1997) (25)
- A canonical factorization for meromorphic Herglotz functions on the unit disk and sum rules for Jacobi matrices (2004) (25)
- Sum rules and spectral measures of Schrödinger operators with L2 potentials (2009) (25)
- Schrödinger Operators with Few Bound States (2004) (24)
- Aizenman's Theorem for Orthogonal Polynomials on the Unit Circle (2004) (24)
- Limits of zeros of orthogonal polynomials on the circle (2004) (24)
- Quantum Dynamics: From Automorphism to Hamiltonian (2015) (24)
- Mean field upper bound on the transition temperature in multicomponent ferromagnets (1980) (23)
- Bound states and the Szegő condition for Jacobi matrices and Schrödinger operators (2002) (23)
- Natural boundaries and spectral theory (2010) (23)
- Orthogonal polynomials with exponentially decaying recursion coefficients (2006) (23)
- Cantor polynomials and some related classes of OPRL (2015) (23)
- Adiabatic theorems for dense point spectra (1990) (23)
- A comparison of plane rotor and Ising models (1980) (23)
- The Hilbert transform of a measure (2008) (22)
- An inequality among determinants. (1975) (22)
- On the Growth of the Number of Bound States with Increase in Potential Strength (1969) (22)
- Absence of continuous symmetry breaking in a one-dimensional n−2 model (1981) (22)
- Rakhmanov’s theorem and related issues (2005) (22)
- Tosio Kato’s work on non-relativistic quantum mechanics: part 1 (2017) (21)
- Critical Lieb-Thirring Bounds in Gaps and the Generalized Nevai Conjecture for Finite Gap Jacobi Matrices (2010) (21)
- Eigenvalue bounds in the gaps of Schrödinger operators and Jacobi matrices (2007) (21)
- Convergence in trace ideals (1981) (21)
- Explicit Construction of Solutions of the Modified Kadomtsev-Petviashvili Equation (1991) (20)
- Localization for off-diagonal disorder and for continuous Schrödinger operators (1987) (20)
- Advanced Complex Analysis: A Comprehensive Course in Analysis, Part 2B (2015) (19)
- OPERATORS WITH SINGULAR CONTINUOUS SPECTRUM : III (2002) (19)
- Correlation Inequalities and the Mass Gap in P(φ) 2 .: II. Uniqueness of the Vacuum for a Class of Strongly Coupled Theories (1975) (19)
- Scattering theory and quadratic forms: On a theorem of Schechter (1977) (19)
- Positivity of the Hamiltonian semigroup and the construction of Euclidean region fields (1973) (18)
- A counterexample to the paramagnetic conjecture (1979) (18)
- Stability of gaps for periodic potentials under variation of a magnetic field (1984) (18)
- Finite Gap Jacobi Matrices, III. Beyond the Szegő Class (2011) (18)
- Convergence of time dependent perturbation theory for autoionizing states of atoms (1971) (18)
- Spectral properties of random Schrödinger operators with unbounded potentials (1993) (18)
- Franco-American meeting on the mathematics of random and almost periodic potentials (1984) (18)
- Internal Lifschitz tails (1987) (17)
- Unitaries permuting two orthogonal projections (2017) (17)
- On a theorem of Kac and Gilbert (2004) (17)
- Convergence of regularized, renormalized perturbation series for super-renormalizable field theories (1969) (17)
- Necessary and sufficient conditions in the spectral theory of Jacobi matrices and Schrödinger operators (2004) (16)
- Periodic Jacobi matrices on trees (2019) (16)
- Large deviations and the Lukic conjecture (2017) (16)
- Poncelet's theorem, paraorthogonal polynomials and the numerical range of compressed multiplication operators (2018) (16)
- Asymptotics of Chebyshev polynomials, II: DCT subsets of R (2019) (16)
- Large deviations and sum rules for spectral theory. A pedagogical approach (2016) (15)
- Finite Gap Jacobi Matrices: A Review (2013) (15)
- Rigorous perimeter law upper bound on Wilson loops (1982) (15)
- Meromorphic Szegő functions and asymptotic series for Verblunsky coefficients (2005) (15)
- Equality of the density of states in a wide class of tight-binding Lorentzian random models (1983) (15)
- A spectral mapping theorem for tensor products of unbounded operators (1972) (14)
- Complete separability of the Stark problem in hydrogen (1979) (14)
- Fluctuations in $P(\phi)_1$ Processes (1976) (14)
- Determination of Eigenvalues by Divergent Perturbation Series (1971) (14)
- Tosio Kato’s Work on Non-relativistic Quantum Mechanics: A Brief Report (2017) (13)
- Regularity and the Cesàro-Nevai class (2007) (13)
- N body scattering in the two-cluster region (1978) (12)
- Bounds on Total Cross Sections in Atom-Atom and Atom-Ion Collisions by Geometric Methods (1980) (11)
- Pointwise bounds on eigenfunctions and wave packets in N-body quantum systems. VI. Asymptotics in the two-cluster region (1980) (11)
- Asymptotic Series for the Ground State Energy of Schrödinger Operators (1993) (11)
- Uniform Crossnorms (2004) (11)
- Proof of the Strong Scott Conjecture for Chandrasekhar Atoms (2019) (11)
- Boundary conditions for the $P(\phi )_2$ euclidean field theory (1976) (11)
- Large coupling behaviour of the Lyapunov exponent for tight binding one-dimensional random systems (1983) (11)
- A Feynman-Kac Formula for Unbounded Semigroups (1999) (11)
- Krein's spectral shift function and fredholm determinants as efficient methods to study supersymmetric quantum mechanics (1987) (11)
- SUMMABILITY METHODS, THE STRONG ASYMPTOTIC CONDITION, AND UNITARITY IN QUANTUM FIELD THEORY. (1972) (11)
- Ultracontractive Semigroups and Some Problems in Analysis (1986) (11)
- Similarity Between Two Projections (2017) (11)
- Relative rearrangement on a finite measure space: application to weighted spaces and to PDE (1997) (11)
- Tosio Kato’s work on non-relativistic quantum mechanics: part 2 (2018) (11)
- On the selfadjointness of Dirac operators with anomalous magnetic moment (1985) (10)
- Stability of Asymptotics of Christoffel–Darboux Kernels (2013) (10)
- The (²ⁿ)₂ field Hamiltonian for complex coupling constant (1972) (10)
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