現代數學物理方法（第2捲） [Methods of Modern Mathematical Physics II] 下載 mobi epub pdf 電子書 2024

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內容簡介

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.

目錄

PrefaceIntroductionContents of Other VolumesIX: THE FOURIER TRANSFORM1. The Fourier transform on（Rn）andc'（Rn）,cconvolutions2. The range of the Fourier transform: Classical spaces3. The range of the Fourier transform: Analyticity4. Lp EstimatesAppendix Abstract interpolation5.Fundamental solutions of partial differential equations with constant coefficients6. Elliptic regularity7. The free Hamiltonian for nonrelativistic quantum mechanics8. The Garding-Wightman axiomsAppendix Lorentz invariant measures9. Restriction to submanifolds10. Products of distributions,wave front sets,and oscillatory integralsNotesProblems1Reader's GuideX:SELF-ADJOINTNESS AND THE EXISTENCE OF DYNAMICS1. Extensions of symmetric operatorsAppendix Motion on a half-line,limit point-limit circle methods2. Perturbations of self-adjoint operators3. Positivity and self-adjointness I: Quadratic forms4. Positivity and self-adjointness II: Pointwise positivity5. The commutator theorem6. Analytic vectors7. Free quantum fieldsAppendix The Weyl relations for the free field8. Semigroups and their generators9. Hypercontractive semigroups10. Graph Limits11. The Feynman-Kac formula12. Time-dependent Hamiltonians13. Classical nonlinear wave equations14. The Hilbert space approach to classical mechanicsNotesProblemsReader's GuideList of SymbolsIndex

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