IV: Analysis of Operators

BESTSELLER of the XXth Century in Mathematical Physics voted on by participants of the XIIIth International Congress on Mathematical Physics This revision will make this book mroe attractive as a textbook in functional analysis. Further refinement of coverage of physical topics will also reinforce its well-established use as a course book in mathemtical physics.

Preface

vii

Introduction

ix

Contents of Other Volumes

xv

Perturbation of Point Spectra

Finite-dimensional perturbation theory

1

(9)

Appendix Algebraic and geometric multiplicity of eigenvalues of finite matrices

9

(1)

Regular perturbation theory

10

(15)

Asymptotic perturbation theory

25

(13)

Summability methods in perturbation theory

38

(7)

Spectral concentration

45

(6)

Resonances and the Fermi golden rule

51

(24)

Notes

60

(9)

Problems

69

(6)

Spectral Analysis

The min-max principle

75

(4)

Bound states of Schrodinger operators I: Quantitative methods

79

(7)

Bound states of Schrodinger operators II: Qualitative theory

86

(20)

Is σdisc (H) finite or infinite?

86

(4)

Bounds on N(V) in the central case

90

(8)

Bounds on N(V) in the general two-body case

98

(8)

Locating the essential spectrum I: Weyl's theorem

106

(14)

Locating the essential spectrum III: The HVZ theorem

120

(16)

The absence of singular continuous spectrum I: General theory

136

(5)

The absence of singular continuous spectrum II: Smooth perturbations

141

(27)

Weakly coupled quantum systems

151

(6)

Positive commutators and repulsive potentials

157

(6)

Local Smoothness and wave operators for repulsive potentials

163

(5)

The absence of singular continuous spectrum III: Weighted L2 spaces

168

(9)

The spectrum of tensor products

177

(6)

The absence of singular continuous spectrum IV: Dilation analytic potentials

183

(8)

Properties of eigenfunctions

191

(10)

Nondegeneracy of the ground state

201

(21)

Appendix 1 The Beurling-Deny criteria

209

(3)

Appendix 2 The Levy-Khintchine formula

212

(10)

Absence of positive eigenvalues

222

(22)

Appendix Unique continuation theorems for Schrodinger operators

239

(5)

Compactness criteria and operators with compact resolvent

244

(16)

The asymptotic distribution of eigenvalues

260

(19)

Schrodinger operators with periodic potentials

279

(37)

An introduction to the spectral theory of non-self-adjoint operators

316

(71)

Notes

338

(26)

Problems

364

(23)

List of Symbols

387

(2)

Index

389

What is included with this book?

The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.

FREE SHIPPING

Amazon no longer offers textbook rentals. We do!

IV: Analysis of Operators

Summary

Table of Contents

Supplemental Materials