Twelve tales in mathematical physics: An expanded Heineman prize lecture

DOI10.1063/5.0056008OpenAlexW4213001111MaRDI QIDQ5056854

Publication date: 8 December 2022

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2011.12335

Mathematics Subject Classification ID

Development of contemporary mathematics (01A65) Quantum theory (81-XX) Statistical mechanics, structure of matter (82-XX)

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Decimations for two-dimensional Ising and rotator models

Cites Work

Korteweg‐devries equation and generalizations. VI. methods for exact solution
Pointwise Bounds on Eigenfunctions and Wave Packets in N-Body Quantum Systems. II
Orthogonal polynomials. II
Pointwise Bounds on Eigenfunctions and Wave Packets in N-Body Quantum Systems. III
The asymptotic eigenvalue distribution for non-smooth elliptic operators
An inequality among determinants
Logarithmic Sobolev Inequalities
The asymptotic distribution of eigenvalues of the Laplace operator in an unbounded domain
Bounds on the eigenvalues of the Laplace and Schroedinger operators
NON-LINEAR EQUATIONS OF KORTEWEG-DE VRIES TYPE, FINITE-ZONE LINEAR OPERATORS, AND ABELIAN VARIETIES
Analysis With Weak Trace Ideals and the Number of Bound States of Schrodinger Operators
A time-dependent approach to the completeness of multiparticle quantum systems
ESTIMATES OF SINGULAR NUMBERS OF INTEGRAL OPERATORS
Quasitriangular Matrices
Absolutely continuous spectrum for one-dimensional Schrödinger operators with slowly decaying potentials: Some optimal results
Genericity of Certain Classes of Unitary and Self-Adjoint Operators
On the Leading Correction of the Statistical Atom: Lower Bound
The calculus of snakes and the combinatorics of Bernoulli, Euler and Springer numbers of Coxeter groups
Asymptotic Completeness of N-Particle Long-Range Scattering
A Forbidden Set for Embedded Eigenvalues
Singular continuous spectrum is generic
Asymptotische Integration der Differentialgleichung des Thomas-Fermischen Atoms
Spectral averaging and the Krein spectral shift
Schrödinger operators with dynamically defined potentials
Dynamics and spectral theory of quasi-periodic Schrödinger-type operators
Bounds on Total Cross Sections in Atom-Atom and Atom-Ion Collisions by Geometric Methods
Decay of Correlations in Ferromagnets
Quantum Magnetic Hamiltonians with Remarkable Spectral Properties
Imbedded singular continuous spectrum for Schrödinger operators
Pointwise Bounds on Eigenfunctions and Wave Packets in N-Body Quantum Systems. I
A diamagnetic inequality for semigroup differences
HIGHER ORDER TRACE RELATIONS FOR SCHRÖDINGER OPERATORS
LOCALIZATION AT WEAK DISORDER: SOME ELEMENTARY BOUNDS
CYCLIC VECTORS IN THE ANDERSON MODEL
L p Norms of the Borel Transform and the Decomposition of Measures
Operators with singular continuous spectrum, VI. Graph Laplacians and Laplace-Beltrami operators
Uniqueness theorems in inverse spectral theory for one-dimensional Schrödinger operators
Operators with singular continuous spectrum, V. Sparse potentials
Inverse spectral analysis with partial information on the potential, II. The case of discrete spectrum
Remarks on periodic Jacobi matrices on trees
Proof of the Strong Scott Conjecture for Chandrasekhar Atoms
Schrodinger Operators with Purely Discrete Spectrum
Mathematics of Quantum Chaos in 2019
Mathematical Theory of Scattering Resonances
Renormalization Group and Problem of Radiation
Fine structure of the zeros of orthogonal polynomials IV: A priori bounds and clock behavior
Fine structure of the zeros of orthogonal polynomials III: Periodic recursion coefficients
On the perturbation of spectra
The virial theorem and its application to the spectral theory of Schrödinger operators
Partially Alternate Derivation of a Result of Nelson
On positive eigenvalues of one‐body schrödinger operators
A<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>λ</mml:mi><mml:mrow><mml:msup><mml:mrow><mml:mi>ϕ</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>Quantum Field Theory without Cutoffs. I
Absolute Continuity of Hamiltonian Operators with Repulsive Potential
Tensor products of closed operators on Banach spaces
Uniform crossnorms
Operators with singular continuous spectrum. IV: Hausdorff dimensions, rank one perturbations, and localization
Fine structure of the zeros of orthogonal polynomials. II: OPUC with competing exponential decay
On the distribution of zeros of polynomials orthogonal on the unit circle
Störungstheorie der Spektralzerlegung. I. Analytische Störung der isolierten Punkteigenwerte eines beschränkten Operators
Perturbation des transformations autoadjointes dans l'espace de Hilbert
Perturbation theory of semi-bounded operators
Cwikel's bound reloaded
Carleman estimates and unique continuation for second-order elliptic equations with nonsmooth coefficients
Asymptotics of orthonormal polynomials in the presence of a denumerable set of mass points
The quantum N-body problem
Schrödinger semigroups
The uncertainty principle
Reflections on the Baker–Gammel–Wills (Padé) Conjecture
JACOBI MATRICES WITH RANDOM POTENTIALS TAKING FINITELY MANY VALUES
An Inverse Sturm–Liouville Problem with Mixed Given Data
On the energy of a large atom
Noncommutative microlocal analysis. I
Nonselfadjoint Schrödinger operators with singular first-order coefficients
On a Problem of Weyl in the Theory of Singular Sturm-Liouville Equations
On convergence to the møller wave operators
On a theorem of Weyl-von Neumann
On the existence and the unitary property of the scattering operator
Wave operators in multichannel scattering
Euclidean Quantum Electrodynamics
Perturbation of continuous spectra by Trace class operators
Growth properties of solutions of the reduced wave equation with a variable coefficient
Schrödinger Scattering Amplitude. I
Statistical Theory of the Energy Levels of Complex Systems. I
UNITARY REPRESENTATIONS OF NILPOTENT LIE GROUPS
Instantons, double wells and large deviations
Multiple wells in the semi-classical limit I
Basic Complex Analysis
Shape resonances for distortion analytic schrödinger operators
Quantal phase factors accompanying adiabatic changes
Thomas-fermi and related theories of atoms and molecules
One-dimensional wave equations in disordered media
A multiparticle Coulomb system with bound state at threshold
Stability of gaps for periodic potentials under variation of a magnetic field
Sobolev Embeddings for Generalized Ridged Domains
Singular continuous spectrum under rank one perturbations and localization for random hamiltonians
Résonances en limite semi-classique
On subordinacy and analysis of the spectrum of Schrödinger operators with two singular endpoints
On the Stability of Molecules in the Thomas-Fermi Theory
Borel summability and indeterminacy of the Stieltjes moment problem: Application to the anharmonic oscillators
Complete separability of the Stark problem in hydrogen
An improvement of Watson’s theorem on Borel summability
Lower semicontinuhy of positive quadratic forms
Resonances in one-dimensional Stark effect and continued fractions
Brownian motion and harnack inequality for Schrödinger operators
Most Monotone Functions are Singular
Singular continuous spectrum for a class of almost periodic Jacobi matrices
Summation of divergent series by order dependent mappings: Application to the anharmonic oscillator and critical exponents in field theory
Intervals of Dense Point Spectrum for Spherically Symmetric Schrödinger Operators of the Type −δ+cos|x |
The Neumann Laplacian of a Jelly Roll
Open problems and conjectures related to the theory of mathematical quasicrystals
Asymptotics of Chebyshev polynomials. I: Subsets of \({\mathbb {R}}\)
Mathematical study of scattering resonances
Critical Lieb-Thirring bounds in gaps and the generalized Nevai conjecture for finite gap Jacobi matrices
On a theorem of Kac and Gilbert
Semiclassical analysis of low lying eigenvalues. II: Tunneling
The twisting trick for double well Hamiltonians
The rotation number for finite difference operators and its properties
A new criterion for scattering theory
The Hilbert transform of a measure
Natural boundaries and spectral theory
Bulk universality and clock spacing of zeros for ergodic Jacobi matrices with absolutely continuous spectrum
The absolutely continuous spectrum of Jacobi matrices
Spectral properties of limit-periodic Schrödinger operators
Finite gap Jacobi matrices. II: The Szegő class
A new approach to universality limits involving orthogonal polynomials
Analytic continuation of eigenvalues of a quartic oscillator
An atomic energy lower bound that agrees with Scott's correction
Relativistic Schrödinger operators: Asymptotic behavior of the eigenfunctions
On the measure of the spectrum for the almost Mathieu operator
Asymptotic behaviour of eigenfunctions for multiparticle Schrödinger operators
On the Schrödinger equation and the eigenvalue problem
Une méthode pour minorer les exposants de Lyapounov et quelques exemples montrant le caractère local d'un théorème d'Arnold et de Moser sur le tore de dimension 2
Singuläre elliptische Differentialoperatoren in Hilbertschen Räumen
Perturbation of the continuous spectrum and unitary equivalence
Espaces de Dirichlet. I: Le cas élémentaire
On finite-dimensional perturbations of self-adjoint operators
Perturbation of continuous spectra by unbounded operators. II
Uniqueness of the self-adjoint extension of singular elliptic differential operators
Nonclassical eigenvalue asymptotics
Schrödinger operators with an electric field and random or deterministic potentials
Log Hölder continuity of the integrated density of states for stochastic Jacobi matrices
Geometric analysis of \(\phi^ 4\) fields and Ising models. I, II
Kotani theory for one dimensional stochastic Jacobi matrices
Almost periodic Schrödinger operators. II: The integrated density of states
Almost periodic Schrödinger operators: A review
Remark on the continuity of the density of states of ergodic finite difference operators
Some Jacobi matrices with decaying potential and dense point spectrum
Some quantum operators with discrete spectrum but classically continuous spectrum
Asymptotic completeness for N-body short-range quantum systems: A new proof
Resonances for nonanalytic potentials
The Fermi golden rule and its form at thresholds in odd dimensions
Rank one perturbations and the zeros of paraorthogonal polynomials on the unit circle
Fine structure of the zeros of orthogonal polynomials. I: A tale of two pictures
The phase transition in the one-dimensional Ising model with \(1/r^2\) interaction energy
Sum rules via large deviations
Regularity of the invariant measure and of the density of states in the one-dimensional Anderson model
Absence of ballistic motion
Two extensions of Lubinsky's universality theorem
Eigenvalue bounds for perturbations of Schrödinger operators and Jacobi matrices with regular ground states
Gibbsian random fields for lattice systems with pairwise interactions.
Perturbations of orthogonal polynomials with periodic recursion coefficients
Equality of the spectral and dynamical definitions of reflection
Weak convergence of CD kernels and applications
Universality limits in the bulk for arbitrary measures on compact sets
Universality and fine zero spacing on general sets
A new proof of the Mourre estimate
Absence of continuous symmetry breaking in a one-dimensional n**-2 model
Cantor spectrum for the almost Mathieu equation
One-dimensional Schrödinger operators with random or deterministic potentials: New spectral types
Subharmonicity of the Lyapunov index
Absence of diffusion in the Anderson tight binding model for large disorder or low energy
On the essential spectrum of Schrödinger operators
Krein's formula and one-dimensional multiple-well
Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians
Anderson localization for multi-dimensional systems at large disorder or large energy
Harmonic analysis on SL(2,R) and smoothness of the density of states in the one-dimensional Anderson model
Universal lower bounds on eigenvalue splittings for one dimensional Schrödinger operators
A new proof of the Cwikel-Lieb-Rosenbljum bound
An exactly solvable model of a multidimensional incommensurate structure
Some connections between excursion theory and the discrete Schrödinger equation with random potentials
Unique continuation and absence of positive eigenvalues for Schrödinger operators. (With an appendix by E. M. Stein)
Almost periodic Schrödinger operators. IV. The Maryland model
Semiclassical analysis of low lying eigenvalues. III: Width of the ground state band in strongly coupled solids
A supersymmetric transfer matrix and differentiability of the density of states in the one-dimensional Anderson model
Localization in general one dimensional random systems. I: Jacobi matrices
Dense point spectra of Schrödinger and Dirac operators
A short proof of the local Atiyah-Singer index theorem
Exponential dichotomy, rotation number, and linear differential operators with bounded coefficients
Lifshitz tails for periodic plus random potentials
Localization for off-diagonal disorder and for continuous Schrödinger operators
Localization in general one-dimensional random systems. II: Continuum Schrödinger operators
Caractérisation du spectre essentiel de l'opérateur de Schrödinger avec un champ magnétique. (Characterization of the essential spectrum of the Schrödinger operator with a magnetic field)
Appearance of a purely singular continuous spectrum in a class of random Schrödinger operators
Corrections to the classical behavior of the number of bound states of Schrödinger operators
The N-particle scattering problem: asymptotic completeness for short- range systems
One-dimensional Schrödinger operators with random decaying potentials
Semiclassical analysis of low lying eigenvalues. IV. The flea on the elephant
Sharp exponential bounds on resonances states and width of resonances
Stochastic Schrödinger operators and Jacobi matrices on the strip
Comparison theorems for the gap of Schrödinger operators
Distribution of poles for scattering on the real line
On subordinacy and analysis of the spectrum of one-dimensional Schrödinger operators
Geometric theory of Stark resonances in multielectron systems
Why the circle is connected: An introduction to quantized topology
Pointwise bounds on eigenfunctions and wave packets in N-body quantum systems. IV
Regularity properties of Schrödinger and Dirichlet semigroups
On the bound state of Schrödinger operators in one dimension
Spectral properties of disordered systems in the one-body approximation
On the Cook-Kuroda criterion in scattering theory
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Similarity between two projections
Tosio Kato's work on non-relativistic quantum mechanics. I
Existence of Hartree-Fock excited states for atoms and molecules
Universal hierarchical structure of quasiperiodic eigenfunctions
Unique continuation for many-body Schrödinger operators and the Hohenberg-Kohn theorem
Unitaries permuting two orthogonal projections
Chern numbers, quaternions, and Berry's phases in Fermi systems
A trace formula for multidimensional Schrödinger operators
Anderson localization for Bernoulli and other singular potentials
Solutions of Hartree-Fock equations for Coulomb systems
Internal Lifschitz tails
Stark effect in multielectron systems: Non-existence of bound states
Trace class perturbations and the absence of absolutely continuous spectra
Spectral behavior of quasi periodic potentials
Exponential bounds and absence of positive eigenvalues for N-body Schrödinger operators
On the absence of spontaneous breakdown of continuous symmetry for equilibrium states in two dimensions
Comportement asymptotique des valeurs propres d'opérateurs du type Schrödinger à potentiel dégénérée
A new approach to inverse spectral theory. II: General real potentials and the connection to the spectral measure
Resonances in one dimension and Fredholm determinants
Operators with singular continuous spectrum. I: General operators
Absolute summability of the trace relation for certain Schrödinger operators
Crossed products of \(C^\ast\)-algebras and spectral analysis of quantum Hamiltonians
Lieb-Thirring inequalities for Jacobi matrices
On the coexistence of absolutely continuous and singular continuous components of the spectral measure for some Sturm--Liouville operators with square summable potential
A canonical factorization for meromorphic Herglotz functions on the unit disk and sum rules for Jacobi matrices
A new proof of Poltoratskii's theorem
Rank one perturbations at infinite coupling
Rank one perturbations with infinitesimal coupling
Splitting of Landau levels in the presence of external potentials
Singular continuous spectrum for palindromic Schrödinger operators
Spectral analysis of \(N\)-body Stark Hamiltonians
Pure point spectrum under 1-parameter perturbations and instability of Anderson localization
Operators with singular continuous spectrum. VII: Examples with borderline time decay
Local fluctuation of the spectrum of a multidimensional Anderson tight binding model
On the Lieb-Thirring constants \(L_{\gamma, 1}\) for \(\gamma \geq 1/2\)
Absolutely continuous spectra of one-dimensional Schrödinger operators and Jacobi matrices with slowly decreasing potentials
Finite gap Jacobi matrices. I: The isospectral torus
Generalized Floquet theory for stationary Schrödinger operators in one dimension
A new approach to inverse spectral theory. I: Fundamental formalism
Metal-insulator transition for the almost Mathieu operator
The nonlinear Schrödinger equation for orthonormal functions. II: Application to Lieb-Thirring inequalities
Marginal triviality of the scaling limits of critical 4D Ising and \(\phi_4^4\) models
The \(P(\phi)_2\) Euclidean quantum field theory as classical statistical mechanics. I.
The inverse approach to Dirac-type systems based on the \(A\)-function concept
On point spectrum of critical almost Mathieu operators
Existence of a phase-transition in a one-dimensional Ising ferromagnet
The free Markoff field
Axioms for Euclidean Green's functions
Almost periodic Schrödinger operators. III: The absolutely continuous spectrum in one dimension
Radiation conditions and scattering theory for \(N\)-particle Hamiltonians
The statistical distribution of the zeros of random paraorthogonal polynomials on the unit circle
Connectedness of the isospectral manifold for one-dimensional half-line Schrödinger operators
The Ten Martini problem
Divergence of perturbation theory for bosons
Finite gap Jacobi matrices. III: Beyond the Szegő class
Cwikel's theorem and the CLR inequality
The classical limit of quantum spin systems
Correlation inequalities and the mass gap in \(P(\phi)_2\). I: Domination by the two point function
Eigenvalue bounds in the gaps of Schrödinger operators and Jacobi matrices
Equilibrium measures and capacities in spectral theory
Applications of universality limits to zeros and reproducing kernels of orthogonal polynomials
The essential spectrum of Schrödinger, Jacobi, and CMV operators
A general resonance theory based on Mourre's inequality
Simplicity of singular spectrum in Anderson-type Hamiltonians
Discreteness of spectrum and positivity criteria for Schrödinger operators
Generic sets in spaces of measures and generic singular continuous spectrum for Delone Hamiltonians
Jost functions and Jost solutions for Jacobi matrices. I: A necessary and sufficient condition for Szegő asymptotics
On exponential representation of analytic functions in the upper half- plane with positive imaginary part
Wave operators and similarity for some non-selfadjoint operators
Hermitian vector bundles and the equidistribution of the zeroes of their holomorphic section
Spectral concentration for self-adjoint operators
Statistical mechanics of a one-dimensional lattice gas
Zur Spektraltheorie von Sturm-Liouville-Operatoren
Boson fields with nonlinear selfinteraction in two dimensions
Second order concentration near the binding energy of the helium Schrödinger operator
A note on Kato's uniqueness criterion for Schrödinger operator self- adjoint extensions
Existence of phase transitions for quantum lattice systems
Extremal polynomials associated with a system of curves in the complex plane
Embedded eigenvalues and virtual poles
The \(\lambda (\varphi^ 4)_ 2\) quantum field theory without cutoffs. II: The field operators and the approximate vacuum
Geometrical operations of Whitehead groups
Commutators and scattering theory. I: Repulsive interactions
Some aspects of the Thomas-Fermi equation
Curvature and the eigenforms of the Laplace operator
Construction of nonlinear local quantum processes. I
Spectral properties of many-body Schrödinger operators with dilatation- analytic interactions
A class of analytic perturbations for one-body Schrödinger Hamiltonians
Construction of non-linear local quantum processes. II
A class of orthogonal polynomials
Essential self-adjointness of Schrödinger operators with positive potentials
Quadratic form techniques and the Balslev-Combes theorem
Hypercontra ctive semigroups and two dimensional self-coupled Bose fields
Determination of eigenvalues by divergent perturbation series
Scattering theory for differential operators. I: Operator theory
Schrödinger operators with singular potentials
Spectral properties of Hamiltonian operators
Scattering theory for differential operators. II: Self-adjoint elliptic operators
Resonances in n-body quantum systems with dilatation analytic potentials and the foundations of time-dependent perturbation theory
Construction of quantum fields from Markoff fields
Absence of positive eigenvalues in a class of multiparticle quantum systems
The classical limit of quantum partition functions
Brownian motion, \(L^p\) properties of Schrödinger operators and the localization of binding
Dilation analyticity in constant electric field I. The two body problem
Spectral properties of Schrödinger operators and time-decay of the wave functions
Sur le spectre des opérateurs aux différences finies aléatoires
The local structure of the spectrum of the one-dimensional Schrödinger operator
Comportement semi-classique du spectre des hamiltoniens quantiques elliptiques
Singular continuous measures in scattering theory
The mathematical theory of resonances whose widths are exponentially small
Coupling constant thresholds in nonrelativistic quantum mechanics. I. Short-range two-body case
Unique continuation for Schrödinger operators with unbounded potentials
Coupling constant thresholds in nonrelativistic quantum mechanics. II: Two cluster thresholds in N-body systems
The asymptotics of the gap in the Mathieu equation
Pointwise bounds on eigenfunctions and wave packets in N-body quantum systems. V: Lower bounds and path integrals
Schrödinger operators with magnetic fields. III: Atoms in homogeneous magnetic field
Finite total cross-sections in nonrelativistic quantum mechanics
Dilation analyticity in constant electric field. II: N-body problem, Borel summability
An example of a Schrödinger equation with almost periodic potential and nowhere dense spectrum
Spectral analysis of N-body Schrödinger operators
Pointwise bounds on eigenfunctions and wave packets in N-body quantum systems. VI: Asymptotics in the two-cluster region
Almost periodic Schrödinger operators. I: Limit periodic potentials
Transient and recurrent spectrum
Absence of singular continuous spectrum for certain self-adjoint operators
Resonances in the Stark effect of atomic systems
The rotation number for almost periodic potentials
Supersymmetry and Morse theory
Geometric methods in the quantum many-body problem. Nonexistence of very negative ions
Spectral theory of one-dimensional Schrödinger operators with strongly fluctuating potentials
The essential spectrum of Neumann Laplacians on some bounded singular domains
Eigenvalue asymptotics of the Neumann Laplacian of regions and manifolds with cusps
Spectral properties of Neumann Laplacian of horns
Space-time picture of semiclassical resonances
A relation between a.c. spectrum of ergodic Jacobi matrices and the spectra of periodic approximants
The quantum mechanical virial theorem and the absence of positive energy bound states of Schrödinger operators
Puiseux series for resonances at an imbedded eigenvalue
The spectrum of Hill's equation
The bound state of weakly coupled Schrödinger operators in one and two dimensions
Unitary equivalence of Stark Hamiltonians
On the decoupling of finite singularities from the question of asymptotic completeness in two body quantum systems
Correlation inequalities on some partially ordered sets
Invariant domains for the time-dependent Schrödinger equation
Spectral and scattering theory of Schrödinger operators related to the Stark effect
Scattering theory and quadratic forms: On a theorem of Schechter
Local distortion technique, resonances, and poles of the S-matrix
Weak type estimates for singular values and the number of bound states of Schrödinger operators
On the absorption of eigenvalues by continuous spectrum in regular perturbation problems
A pure point spectrum of the stochastic one-dimensional Schrödinger operator
Bounds on the number of eigenvalues of the Schrödinger operator
Domination of semigroups and generalization of Kato's inequality
A generalization of the Birman trace theorem
Asymptotic completeness for quantum mechanical potential scattering. I: Short range potentials
Applications of a commutation formula
Scattering theory for systems with different spatial asymptotics on the left and right
Remarks on Schrödinger operators with vector potentials
Schrödinger operators with magnetic fields. I: General interactions
Phase space analysis of simple scattering systems: extensions of some work of Enss
Pointwise bounds for Schrödinger eigenstates
Remarks on the Schrödinger operator with singular complex potentials
Separation of center of mass in homogeneous magnetic fields
Geometric methods in multiparticle quantum systems
A canonical decomposition for quadratic forms with applications to monotone convergence theorems
Kato's inequality and the comparison of semigroups
The absolute continuous spectrum of one-dimensional Schrödinger operators with decaying potentials
Modified Prüfer and EFGP transforms and the spectral analysis of one-dimensional Schrödinger operators
The Thomas-Fermi theory of atoms, molecules and solids
Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schrödinger operators
A sharp bound for an eigenvalue moment of the one-dimensional Schrödinger operator
Almost periodic Jacobi matrices with homogeneous spectrum, infinite dimensional Jacobi inversion, and Hardy spaces of character-automorphic functions
On the absolutely continuous spectrum of one-dimensional Schrödinger operators with square summable potentials
Localization at large disorder and at extreme energies: an elementary derivation
Stark resonances: Asymptotics and distributional Borel sum
Spectral properties of random Schrödinger operators with unbounded potentials
Asymptotics of the ground state energies of large Coulomb systems
Asymptotic completeness of long-range \(N\)-body quantum systems
Charge deficiency, charge transport and comparison of dimensions
The index of a pair of projections
Zero measure spectrum for the almost Mathieu operator
On pairs of projections in a Hilbert space
Operators with singular continuous spectrum. II: Rank one operators
Operators with singular continuous spectrum. III: Almost periodic Schrödinger operators
The \(\xi\) function
Duality and singular continuous spectrum in the almost Mathieu equation
\(m\)-functions and inverse spectral analysis for finite and semi-infinite Jacobi matrices
Continuity of the Lyapunov exponent for quasiperiodic operators with analytic potential
Sum rules for Jacobi matrices and their applications to spectral theory
Cantor spectrum for the almost Mathieu operator
Bound states and the Szegő condition for Jacobi matrices and Schrödinger operators.
Sum rules and the Szegő condition for orthogonal polynomials on the real line
Inverse spectral theory for one-dimensional Schrödinger operators: The \(A\) function
A new approach to inverse spectral theory. III: Short-range potentials
On local Borg-Marchenko uniqueness results
Spectral structure of Anderson type Hamiltonians
Sharp Lieb-Thirring inequalities in high dimensions.
Phase transitions for \(\phi_2^4\) quantum fields
Large deviations and sum rules for spectral theory: a pedagogical approach
Control of fracture at the interface of dissimilar materials using randomly oriented inclusions and networks
Large deviations and the Lukic conjecture
Eigenvalue bounds for Schrödinger operators with complex potentials II
Spectral theory of extended Harper's model and a question by Erdős and Szekeres
Sharp phase transitions for the almost Mathieu operator
Notes towards the construction of nonlinear relativistic quantum fields. II: The basic nonlinear functions in general space-times
Noncommuting Random Products
Spectral Concentration and Virtual Poles
Smooth operators and commutators
ON THE SPECTRUM OF THE ONE-DIMENSIONAL SCHRÖDINGER EQUATION WITH A RANDOM POTENTIAL
Spectral Concentration and Virtual Poles. II
A spectral mapping theorem for tensor products of unbounded operators
The (φ 2n ) 2 Field Hamiltonian for Complex Coupling Constant
Perturbation of embedded eigenvalues
Completeness of the wave operators in the repulsive N-body problem
Some Schrödinger operators with dense point spectrum
On Positive Harmonic Functions
On Ising's model of ferromagnetism
On the perturbation of continuous spectra
Some theorems on perturbation theory
Fundamental Properties of Hamiltonian Operators of Schrodinger Type
On the Existence of Solutions of the Helium Wave Equation
Divergence of Perturbation Theory in Quantum Electrodynamics
On the Number of Bound States in a Central Field of Force
Statistical Theory of Equations of State and Phase Transitions. II. Lattice Gas and Ising Model
The λφ24 Quantum Field Theory without Cutoffs. IV. Perturbations of the Hamiltonian
Harmonic Analysis
Operator Theory
Potential theory
Bounded eigenfunctions and absolutely continuous spectra for one-dimensional Schrödinger operators
Schrödinger operators with singular magnetic vector potentials
Schrödinger operators with singular magnetic vector potentials
Direct methods in the calculus of variations
Caught by disorder. Bound states in random media
A proof of the local Borg-Marchenko theorem
An introduction to semiclassical and microlocal analysis
Observables at infinity and states with short range correlations in statistical mechanics
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