现代数学物理方法（第2卷）

　　Preface
　　Introduction
　　Contents of Other Volumes
　　IX: THE FOURIER TRANSFORM
　　1. The Fourier transform on（Rn）andc'（Rn）,cconvolutions
　　2. The range of the Fourier transform: Classical spaces
　　3. The range of the Fourier transform: Analyticity
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　　    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 containi…
　查看完整　　

　　Preface
　　Introduction
　　Contents of Other Volumes
　　IX: THE FOURIER TRANSFORM
　　1. The Fourier transform on（Rn）andc'（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-Wightman 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: Quadratic forms
　　4. Positivity and self-adjointness II: Pointwise positivity
　　5. The commutator theorem
　　6. Analytic vectors
　　7. Free quantum fields
　　Appendix The Weyl relations for the free field
　　8. Semigroups and their generators
　　9. Hypercontractive semigroups
　　10. Graph Limits
　　11. The Feynman-Kac formula
　　12. Time-dependent Hamiltonians
　　13. Classical nonlinear wave equations
　　14. The Hilbert space approach to classical mechanics
　　Notes
　　Problems
　　Reader's Guide
　　List of Symbols
　　Index
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　　    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.
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