Note: Intro -- Preface -- A mathematical descendants list -- Publications of Friedrich (Fritz) Gesztesy¹ -- Invariant measures for stochastic differential equations on networks -- 1. Introduction -- 2. Setting of the problem -- 3. The abstract reformulation -- 4. Preliminary results -- 5. A priori estimates. Existence and uniqueness -- 6. The stationary process -- 7. Density of the invariant measure -- Acknowledgments -- References -- On the spectra of large sparse graphs with cycles -- 1. Introduction -- 2. Ensembles of graphs -- 3. Spectral analysis of undirected graphs with cycles -- 4. Spectral analysis of directed graphs with cycles -- 5. Conclusion -- Acknowledgments -- Appendix A. Cavity method applied to random matrices -- References -- Jones' extension operator on Sobolev spaces with partially vanishing traces -- 1. Motivation -- 2. Main results -- References -- Some spectral properties of Rooms and Passages domains and their skeletons -- 1. Introduction -- 2. Rooms & -- Passages domains -- 3. Eigenvalue asymptotics of the Dirichlet and Neumann Laplacians -- 4. A related problem on the skeleton -- 5. A Sturm-Liouville operator -- References -- Finite gap Jacobi matrices: A review -- 1. Introduction -- 2. The Zero Gap Case -- 3. The Isospectral Torus -- 4. Results in the Finite Gap Case -- 5. Methods -- Acknowledgements -- References -- Momentum operators on graphs -- 1. Introduction -- 2. Preliminaries -- 3. Balanced orientability -- 4. Momentum operators -- 5. Momentum operator spectra: finite graphs -- 6. Momentum operator spectra: infinite graphs -- 7. Groups associated with momentum operators -- 8. A two-loop example -- References -- Asymptotic parabolicity for strongly damped wave equations -- 1. Introduction -- 2. Selfadjoint and normal operators -- 3. The main result -- 4. Examples -- References. , On rates in Euler's formula for ₀-semigroups -- 1. Introduction -- 2. Preliminaries and notations -- 3. Functional calculus -- 4. Generalized Stieltjes functions -- 5. Main results -- 6. Optimality of rates -- 7. Appendix -- References -- Construction of a Noncommutative Quantum Field Theory -- 1. Introduction -- 2. Matrix Model -- 3. Ward Identity -- 4. Schwinger-Dyson equation -- 5. Renormalization -- 6. Nonperturbative Construction of this model -- 7. Four-point Schwinger-Dyson equation -- 8. Conclusions -- 9. Acknowledgment -- References -- Periodic conservative solutions for the two-component Camassa-Holm system -- 1. Introduction -- 2. Eulerian and Lagrangian variables -- 3. Lipschitz metric -- 4. Global weak solutions -- References -- A Minimal Uncertainty Product for One Dimensional Semiclassical Wave Packets -- 1. Introduction -- 2. Observations about the Angle of Rotation -- 3. Preliminary Comments about Uncertainty Products -- 4. One Dimensional Semiclassical Wave Packets -- 5. The Rotated Uncertainty Product -- References -- On a transformation of Bohl and its discrete analogue -- 1. Introduction -- 2. The interplay of the Bohl and Green functions -- 3. The discrete form of the Bohl [ ] -- References -- The Morse and Maslov indices for matrix Hill's equations -- 1. Introduction -- 2. Hill's equation and an augmented equation -- 3. A symplectic approach to counting eigenvalues -- 4. Monotonicity of the Maslov index -- 5. The Mathieu equation: an example -- References -- 1-D Schrödinger operators with local point interactions: a review -- 1. Introduction -- 2. Hamiltonians with -interactions -- 2.1. Definition of -interactions -- 2.2. Self-adjointness -- 2.3. Connection with Jacobi matrices -- 2.4. Semiboundedness -- 2.5. Spectral types -- 2.6. Negative spectrum -- 3. Hamiltonians with '-interactions. , 3.1. Definition of '-interactions -- 3.2. Self-adjointness and connection with Jacobi matrices -- 3.3. Semiboundedness -- 3.4. Spectral types -- 3.5. Negative spectrum -- Acknowledgments -- References -- Inverse problem for small oscillations -- 1. Introduction -- 2. Reduction to the inverse spectral problem for Hermitian matrices -- 3. Inverse problems of spectral analysis of Hermitian matrices (preliminary results) -- 4. Solution of inverse problem of spectral analysis for Hermitian matricies -- 5. Examples -- 6. Inverse problem of multichannel scattering -- References -- On the Weyl-Titchmarsh and Livšic functions -- 1. Introduction -- 2. The Livšic and the Weyl-Titchmarsh functions -- 3. The Weyl-Titchmarsh function in the dissipative case -- 4. The characteristic function and the functional model of a dissipative operator -- 5. The spectral analysis of the model dissipative operator -- Appendix A. The spectral properties of the model symmetric operator -- References -- Stability for the inverse resonance problem for the CMV operator -- 1. Introduction -- 2. Preliminaries -- 3. The inverse problem -- 4. Stability -- References -- On a conjecture of A. Bikchentaev -- 1. Introduction and preliminaries -- 2. The main result -- 3. Applications to ideals in (ℳ, ) -- 4. An application to traces -- References -- Spectral theory as influenced by Fritz Gesztesy -- 1. Introduction -- 2. Relativistic corrections -- 3. Singular Weyl-Titchmarsh-Kodaira theory -- 4. Inverse spectral theory and trace formulas -- 5. Commutation methods -- 6. Oscillation theory -- 7. Non-self-adjoint operators -- References -- Prescribed Asymptotic Behavior for Nonlinear Second-Order Dynamic Equations -- 1. Introduction -- 2. Preliminaries -- 3. The Main Results -- 4. Examples -- References.

Note: Intro -- Contents -- I. Gaussian Random Processes, Q-Space and Fock Space -- II: Axioms, I -- III: The Free Euclidean Field -- IV: Axioms, II -- V: Interactions and Transfer Matrices -- VI: Nelson's Symmetry and Its Application -- VII: Dirichlet Boundary Conditions -- VIII: The Lattice Approximation and Its Consequences -- IX: The Classical Ising Approximation and Its Applications -- X: Additional Results and Techniques: A Brief Introduction.

Note: Front Cover -- Methods of Modern Mathematical Physics II: Fourier Analysis, Self-Adjointness -- Copyright Page -- Table of Contents -- Dedication -- Preface -- Introduction -- Contents of Other Volumes -- Chapter IX. The Fourier Transform -- IX.1 The Fourier transform on Y(Rn) and Y'(Rn), convolutions -- IX.2 The range of the Fourier transform: Classical spaces -- IX.3 The range of the Fourier transform : Analyticity -- IX.4 Lp Estimates -- Appendix to IX.4 Abstract interpolation -- IX.5 Fundamental solutions of partial differential equations with constant coefficients -- IX.6 Elliptic regularity -- IX.7 The free Hamiltonian for nonrelativistic quantum mechanics -- IX.8 The Gårding-Wightman axioms -- Appendix to IX.8 Lorentz invariant measures -- IX.9 Restriction to submanifolds -- IX.10 Products of distributions, wave front sets, and oscillatory integrals -- NOTES -- PROBLEMS -- READER'S GUIDE -- Chapter X. Self-Adjointness and the Existence of Dynamics -- X.I Extensions of symmetric operators -- Appendix to X.1 Motion on a half-line, limit point-limit circle methods -- X.2 Perturbations of self-adjoint operators -- X.3 Positivity and self-adjointness I: Quadratic forms -- X.4 Positivity and self-adjointness II : Pointwise positivity -- X.5 Nelson's commutator theorem -- X.6 Analytic vectors -- X.7 Free quantum fields -- Appendix to X.7 The Weyl relations for the free field -- X.8 Semigroups and their generators -- X.9 Hypercontractive semigroups -- X.10 Graph limits -- X.11 The Feynman-Kac formula -- X.12 Time-dependent Hamiltonians -- X.13 Classical nonlinear wave equations -- X.14 The Hilbert space approach to classical mechanics -- NOTES -- PROBLEMS -- READER'S GUIDE -- List of Symbols -- Index.

Note: Front Cover -- Methods of Modern Mathematical Physics IV: Analysis of Operators -- Copyright Page -- Table of Contents -- Dedication -- Preface -- Introduction -- Contents of Other Volumes -- XII: PERTURBATION OF POINT SPECTRA -- 1. Finite-dimensional perturbation theory -- Appendix Algebraic and geometric multiplicity ofeigenvalues of finite matrices -- 2. Regular perturbation theory -- 3. Asymptotic perturbation theory -- 4. Summability methods in perturbation theory -- 5. Spectral concentration -- 6. Resonances and the Fermi golden rule -- Notes -- Problems -- XIII: SPECTRALAN ALYSIS -- 1. The min-max principle -- 2. Bound states of Schrodinger operators I: Quantitative methods -- 3. Bound states of Schrodinger operators II: Qualitative theory -- 4. Locating the essential spectrum I: Weyl's theorem -- 5. Locating the essential spectrum III: The HVZ theorem -- 6. The absence of singular continuous spectrum II:General theory -- 7. The absence of singular continuous spectrum II:Smooth perturbations -- 8. The absence of singular continuous spectrum III:Weighted L2 spaces -- 9. The spectrum of tensor products -- 10. The absence of singular continuous spectrum IV:Dilation analytic potentials -- 11. Properties of eigenfunctions -- 12. Nondegeneracy of the ground state -- Appendix 1 The Beurling-Deny criteria -- Appendix 2 The Levy-Khintchine formula -- 13. Absence of positive eigenvalues -- Appendix Unique continuation theorems for Schrodinger operators -- 14. Compactness criteria and operators with compact resolvent -- 15. The asymptotic distribution of eigenvalues -- 16. Schrodinger operators with periodic potentials -- 17. An introduction to the spectral theory ofnon-self-adjoint operators -- Notes -- Problems -- List of Symbols -- Index.

Note: Front Cover -- Methods of Modern Mathematical Physics III: Scattering Theory -- Copyright Page -- Table of Contents -- Dedication -- Preface -- Introduction -- Contents of Other Volumes -- Chaper XI. SCATTERING THEORY -- 1. An overview of scattering phenomena -- 2. Classical particle scattering -- 3. The basic principles of scattering in Hubert space -- Appendix 1 Stationary phase methods -- Appendix 2 Trace ideal properties of f (x)g( - i v) -- Appendix 3 A general invariance principle for wave operators -- 4. Quantum scattering I: Two-body case -- 5. Quantum scattering II: N-body case -- 6. Quantum scattering III: Eigenfunction expansions -- Appendix Introduction to eigenfunction expansions by theauxiliary space method -- 7. Quantum scattering IV: Dispersion relations -- 8. Quantum scattering V: Central potentials -- Appendix 1 Legendre polynomials and spherical Bessel functions -- Appendix 2 Jost solutions for oscillatory potentials -- Appendix 3 Jost solutions and the fundamental problems ofscattering theory -- 9. Long-range potentials -- 10. Optical and acoustical scattering I: Schrödinger operatormethods -- Appendix Trace class properties of Green's functions -- 11. Optical and acoustical scattering II: The Lax-Phillipsmethod -- Appendix The twisting trick -- 12. The linear Boltzmann equation -- 13. Nonlinear wave equations -- Appendix Conserved currents -- 14. Spin wave scattering -- 15. Quantum field scattering I: The external field -- 16. Quantum field scattering II: The Haag-Ruelle theory -- 17. Phase space analysis of scattering and spectral theory -- Appendix The RAGE theorem -- Notes -- Notes on scattering theory on C*-algebras -- Problems -- MATERIAL PREPRINTED FROM VOLUME IV -- XIII.6 The absence of singular continuous spectrum I: General theory -- XIII.7 The absence of singular continuous spectrum II: Smooth perturbations. , XIII.8 The absence of singular continuous spectrum III:Weighted L2 spaces -- Notes -- Problems -- List of Symbols -- Index.

Note: Cover.

Note: Front Cover -- Methods of Modern Mathematical Physics -- Copyright Page -- Table of Contents -- Preface -- Introduction -- Contents of Other Volumes -- Chapter I. PRELIMINARIES -- 1. Sets and functions -- 2. Metric and normed linear spaces -- Appendix Lim sup and lim inf -- 3. The Lebesgue integral -- 4. Abstract measure theory -- 5. Two convergence arguments -- 6. Equicontinuity -- Notes -- Problems -- Chapter II. HILBERT SPACES -- 1. The geometry of Hilbert space -- 2. The Riesz lemma -- 3. Orthonormal bases -- 4. Tensor products of Hilbert spaces -- 5. Ergodic theory: an introduction -- Notes -- Problems -- Chapter III. BANACH SPACES -- 1 . Definition and examples -- 2. Duals and double duals -- 3. The Hahn-Banach theorem -- 4. Operations on Banach spaces -- 5. The Baire category theorem and its consequences -- Notes -- Problems -- Chapter IV. TOPOLOGICAL SPACES -- 1. General notions -- 2. Nets and convergence -- 3. Compactness -- Appendix The Stone-Weierstrass theorem -- 4. Measure theory on compact spaces -- 5. Weak topologies on Banach spaces -- Appendix Weak and strong measurability -- Notes -- Problems -- Chapter V. LOCALLY CONVEX SPACES -- 1. General properties -- 2. Fréchet spaces -- 3. Functions of rapid decease and the tempered distributions -- Appendix The N-representation for f and f' -- 4. Inductive limits: generalized functions and weak solutions of partial differential equations -- 5. Fixed point theorems -- 6. Applications of fixed point theorems -- 7. Topologies on locally convex spaces: duality theory and the strong dual topology -- Appendix Polars and the Mackey-Arens theorem -- Notes -- Problems -- Chapter VI. BOUNDED OPERATORS -- 1. Topologies on bounded operators -- 2. Adjoints -- 3. The spectrum -- 4. Positive operators and the polar decomposition -- 5. Compact operators -- 6. The trace class and Hilbert-Schmidt ideals. , Notes -- Problems -- Chapter VII. THE SPECTRAL THEOREM -- 1. The continuous functional calculus -- 2. The spectral measures -- 3. Spectral projections -- 4. Ergodic theory revisited: Koopmanism -- Notes -- Problems -- Chapter VIII. UNBOUNDED OPERATORS -- 1. Domains, graphs, adjoints, and spectrum -- 2. Symmetric and self-adjoint operators: the basic criterion for self-adjointness -- 3. The spectral theorem -- 4. Stone's theorem -- 5. Formal manipulation is a touchy business: Nelson's example -- 6. Quadratic forms -- 7. Convergence of unbounded operators -- 8. The Trotter product formula -- 9. The polar decomposition for closed operators -- 10. Tensor products -- 11. Three mathematical problems in quantum mechanics -- Notes -- Problems -- THE FOURIER TRANSFORM -- 1. The Fourier transform on f(Rn) and f'{Rn), convolutions -- 2. The range of the Fourier transform: Classical spaces -- 3. The range of the Fourier transform: Analyticity -- Notes -- Problems -- SUPPLEMENTARY MATERIAL -- II.2. Applications of the Riesz lemma -- III.1. Basic properties of Lp spaces -- IV.3. Proof of Tychonoff's theorem -- IV.4. The Riesz-Markov theorem for X = [0, 1] -- IV.5. Minimization of functionals -- V.5. Proofs of some theorems in nonlinear functional analysis -- VI.5. Applications of compact operators -- VIII.7. Monotone convergence for forms -- VIII.8. More on the Trotter product formula -- Uses of the maximum principle -- Notes -- Problems -- List of Symbols -- Index.

Note: Cover -- Title page -- Contents -- Preface to the second edition -- Preface -- List of symbols -- Functional integration and quantum physics -- Introduction -- The basic processes -- Bound state problems -- Inequalities -- Magnetic fields and stochastic integrals -- Asymptotics -- Other topics -- References -- Index -- Bibliographic supplement -- Bibliography -- Back Cover.

Note: Intro -- I: The Rollnik Condition -- II: The Hamiltonian -- III: Bound States -- IV: Time-Dependent Scattering Theory -- V: Time-Independent Scattering Theory -- VI: Analytic Scattering Theory -- VII: Multiparticle Systems -- Appendix: Some Mathematical Background -- References.