Methods of modern mathematical physics. 2: fourier analysis, self-adjointness

Автор(ы):Reed M., Simon B.
Год изд.:1975
Описание: This volume continues the serie of texts devoted to functional analysis methods in mathematical physics. This volume will serve several purposes: to provide an introduction for graduate students not previously acquainted with the material, to serve as a reference for mathematical physicists already working in the field, and to provide an introduction to various advanced topics which are difficult to understand in the literature. Not all the techniques and applications are treated in the same depth. In general, the authors give a very thorough discussion of the mathematical techniques and applications in quantum mechanics, but provide only an introduction to the problems arising in quantum field theory, classical mechanics, and partial differential equations. To help the reader select which material is important for him, we have provided a "Reader's Guide" at the end of each chapter.
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  1. The Fourier transform on (?) and (?), convolutions [1]
  2. The range of the Fourier transform: Classical spaces [9]
  3. The range of the Fourier transform: Analyticity [15]
  4. If Estimates [27]
    Appendix Abstract interpolation [32]
  5. Fundamental solutions of partial differential equations with constant coefficients [45]
  6. Elliptic regularity [49]
  7. The free Hamiltonian for nonrelativistic quantum mechanics [54]
  8. The Carding-Wightman axioms [61]
    Appendix Lorentz invariant measures [72]
  9. Restriction to submanifolds [76]
  10. Products of distributions, wave front sets, and oscillatory integrals [87]
    Notes [108]
    Problems [120]
    Reader's Guide [133]
  1. Extensions of symmetric operators [135]
    Appendix Motion on a half-line, limit point-limit circle methods [146]
  2. Perturbations of self-adjoint operators [162]
  3. Positivity and self-adjointness I: Quadratic forms [176]
  4. Positivity and self-adjointness II: Pointwise positivity [182]
  5. The commutator theorem [191]
  6. Analytic vectors [200]
  7. Free quantum fields [207]
    Appendix The Weyl relations for the free field [231]
  8. Semigroups and their generators [235]
  9. Ну per contractive semigroups [258]
  10. Graph Limits [268]
  11. The Feynman-Kac formula [274]
  12. Time-dependent Hamiltonians [282]
  13. Classical nonlinear wave equations [293]
  14. The Hilbert space approach to classical mechanics [313]
    Notes [318]
    Problems [338]
    Reader's Guide [349]
List of Symbols [353]
Index [355]
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