Methods of modern mathematical physics. 1: functional analysis

Автор(ы):Reed M., Simon B.
06.10.2007
Год изд.:1980
Описание: This book is the first of a multivolume series devoted to an exposition of functional analysis methods in modern mathematical physics. It describes the fundamental principles of functional analysis and is essentially self-contained, although there are occasional references to later volumes. The authors have included a few applications when they think that they would provide motivation for the reader.
Оглавление:
Methods of modern mathematical physics. 1: functional analysis — обложка книги.
I. PRELIMINARIES
  1. Sets and functions [1]
  2. Metric and normed linear spaces [3]
    Appendix Lim sup and lim inf [11]
  3. The Lebesgue integral [12]
  4. Abstract measure theory [19]
  5. Two convergence arguments [26]
  6. Equicontinuity [28]
    Notes [31]
    Problems [32]
II. HUBERT SPACES
  1. The geometry of Hilbert space [36]
  2. The Riesz lemma [41]
  3. Orthonormal bases [44]
  4. Tensor products of Hilbert spaces [49]
  5. Ergodic theory: an introduction [54]
    Notes [60]
    Problems [63]
III. BANACH SPACES
  1. Definition and examples [67]
  2. Duals and double duals [72]
  3. The Hahn-Banach theorem [75]
  4. Operations on Banach spaces [78]
  5. The Baire category theorem and its consequences [79]
    Notes [84]
    Problems [86]
IV. TOPOLOGICAL SPACES
  1. General notions [90]
  2. Nets and convergence [95]
  3. Compactness [97]
    Appendix The Stone—Weierstrass theorem [103]
  4. Measure theory on compact spaces [104]
  5. Weak topologies on Banach spaces [111]
    Appendix Weak and strong measurability [115]
    Notes [117]
    Problems [119]
V. LOCALLY CONVEX SPACES
  1. General properties [124]
  2. Frechet spaces [131]
  3. Functions of rapid decease and the tempered distributions [133]
    Appendix The N-representation for (?) and (?) [141]
  4. Inductive limits: generalized functions and weak solutions of partial differential equations [145]
  5. Fixed point theorems [150]
  6. Applications affixed point theorems [153]
  7. Topologies on locally convex spaces: duality theory and the strong dual topology [162]
    Appendix Polars and the Mackey-Arens theorem [167]
    Notes [169]
    Problems [173]
VI. BOUNDED OPERATORS
  1. Topologies on bounded operators [182]
  2. Adjoints [185]
  3. The spectrum [188]
  4. Positive operators and the polar decomposition [195]
  5. Compact operators [198]
  6. The trace class and Hilbert-Schmidt ideals [206]
    Notes [213]
    Problems [216]
VII. THE SPECTRAL THEOREM
  1. The continuous functional calculus [221]
  2. The spectral measures [224]
  3. Spectral projections [234]
  4. Ergodic theory revisited: Koopmanism [237]
    Notes [243]
    Problems [245]
VIII. UNBOUNDED OPERATORS
  1. Domains, graphs, adjoints, and spectrum [249]
  2. Symmetric and self-adjoint operators: the basic criterion for self-adjointness [255]
  3. The spectral theorem [259]
  4. Stone's theorem [264]
  5. Formal manipulation is a touchy business: Nelson's example [270]
  6. Quadratic forms [276]
  7. Convergence of unbounded operators [283]
  8. The Trotter product formula [295]
  9. The polar decomposition for closed operators [297]
  10. Tensor products [298]
  11. Three mathematical problems in quantum mechanics [302]
    Notes [305]
    Problems [312]
THE FOURIER TRANSFORM
  1. The Fourier transform on (?) and (?) convolutions [318]
  2. The range of the Fourier transform: Classical spaces [326]
  3. The range of the Fourier transform: Analyticity [332]
    Notes [338]
    Problems [339]
SUPPLEMENTARY MATERIAL
  II.2. Applications of the Riesz lemma [344]
  III.1. Basic properties of (?) spaces [348]
  IV.3. Proof of Tychonoff s theorem [351]
  IV.4. The Riesz-Markov theorem for X=[0,1] [353]
  IV.5. Minimization of'functional [354]
  V.5. Proofs of some theorems in nonlinear functional analysis [363]
  VI.5. Applications of compact operators [368]
  VIII.7. Monotone convergence for forms [372]
  VIII.8. More on the Trotter product formula [377]
    Uses of the maximum principle [382]
    Notes [385]
    Problems [387]
List of Symbols [393]
Index [395]
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Размер:9102604 байт
Язык:ENG
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