This volume continues our series of texts devoted to functional analysis methods in mathematical physics. In Volume I we announced a table of contents for Volume II. However, in the preparation of the material it became clear that we would be unable to treat the subject matter in sufficient depth in one volume. Thus, the volume contains Chapters IX and X; we expect that a third volume will appear in the near future containing the rest of the material announced as "Analysis of Operators." We hope to continue this series with an additional volume on algebraic methods.

Preface

Introduction

Contents of Other Volumes

IX: THE FOURIER TRANSFORM

 1. The Fourier transform on(Rn) and c'(Rn),cconvolutions

 2. The range of the Fourier transform:Classical spaces

 3. The range of the Fourier transform:Analyticity

 4. Lp Estimates

 Appendix Abstract interpolation

 5. Fundamental solutions of partial differential equations with constant coefficients

 6. Elliptic regularity

 7. The free Hamiltonian for nonrelativistic quantum mechanics

 8. The Garding-Wightmanc axioms

 Appendix Lorentz invariant measures

 9. Restriction to submanifolds

 10. Products of distributions,wave front sets,and oscillatory integrals

 Notes

 Problems1

　Reader's Guide

X:SELF-ADJOINTNESS AND THE EXISTENCE OF DYNAMICS

　1. Extensions of symmetric operators

　Appendix Motion on a half-line,limit point-limit circle methods

　2. Perturbations of self-adjoint operators

　3. Positivity and self-adjointness I:Quadrati forms

　4. Positivity and self-adjointness II:Pointwise positivity

　5. The commutator theorem

　6. Analytic vectors

　7. Free quantum fields

　Appendix　TheWeyl　relations　for　thefree　field

　8. Semigroups and their generators

　9. Hypercontractive semigroups

　10. Graph Limits

　11. The Feynman-Kac formula

　12. Time-dependent Hamiltonians

　13. Classical nonlinear wavee quations

　14. The Hilbert space approach to classical mechanics

Notes

Problems

Reader's Guide

List of Symbols

Index