Global Pseudo-Differential Calculus on Euclidean Spaces

2010

Rodino, Luigi , Nicola, Fabio 저자(글)

Birkhauser · 2010년 05월 31일

책 소개

작가정보

저자(글) Rodino, Luigi

저자(글) Nicola, Fabio

목차

• Preface	p. ix
  Introduction	p. 1
  Background material	p. 9
  Basic Facts and Notation	p. 9
  Function Spaces and Fourier Transform	p. 11
  Identities and Inequalities for Factorials and Binomial Coefficients	p. 13
  Global Pseudo-Differential Calculus	p. 15
  Summary	p. 15
  Symbol Classes	p. 19
  Basic Calculus	p. 23
  Action on S	p. 23
  Adjoint and Transposed Operator. Action on S'	p. 29
  Composition of Operators	p. 31
  Global Regularity	p. 34
  Hypoellipticity and Construction of the Parametrix	p. 35
  Slow Variation and Construction of Elliptic Symbols	p. 38
  Boundedness on L2	p. 40
  Sobolev Spaces	p. 41
  Fredholm Properties	p. 45
  Abstract Theory	p. 46
  Pseudo-Differential Operators	p. 50
  Anti-Wick Quantization	p. 51
  Short-Time Fourier Transform and Anti-Wick Operators	p. 52
  Relationship with the Weyl Quantization	p. 54
  Applications to Boundedness on L2 and Almost Positivity of Pseudo-Differential Operators	p. 58
  Sobolev Spaces Revisited	p. 60
  Quantizations of Polynomial Symbols	p. 62
  Notes	p. 64
  ?Pseudo-Differential Operators and H-Polynomials	p. 67
  Summary	p. 67
  ?Pseudo-Differential Operators	p. 70
  ?Elliptic Differential Operators; the Harmonic Oscillator	p. 77
  Asymptotic Integration and Solutions of Exponential Type	p. 82
  H-Polynomials	p. 88
  Quasi-Elliptic Polynomials	p. 94
  Multi-Quasi-Elliptic Polynomials	p. 97
  ?sub>p-Pseudo-Differential Operators	p. 106
  Lp-Estimates	p. 116
  Notes	p. 126
  G-Pseudo-Differential Operators	p. 129
  Summary	p. 129
  G-Pseudo-Differential Calculus	p. 132
  Polyhomogeneous G-Operators	p. 137
  G-Elliptic Ordinary Differential Operators	p. 145
  Other Classes of Globally Regular Operators	p. 148
  Notes	p. 150
  Spectral Theory	p. 153
  Summary	p. 153
  Unbounded Operators in Hilbert spaces	p. 155
  Pseudo-Differential Operators in L2: Realization and Spectrum	p. 158
  Complex Powers	p. 164
  The Resolvent Operator	p. 166
  Proof of Theorem 4.3.6	p. 173
  Hilbert-Schmidt and Trace-Class Operators	p. 177
  Heat Kernel	p. 193
  Weyl Asymptotics	p. 195
  Notes	p. 199
  Non-Commutative Residue and Dixmier Trace	p. 203
  Summary	p. 203
  Non-Commutative Residue for ?Operators	p. 206
  Trace Functional for G-Operators	p. 213
  Dixmier Traceability for General Pseudo-Differential Operators	p. 221
  Notes	p. 224
  Exponential Decay and Holomorpbic Extension of Solutions	p. 227
  Summary	p. 227
  The Function Spaces S?/sup>?/sub>(Rd)	p. 229
  ?Operators and Semilinear Harmonic Oscillators	p. 241
  G-Pseudo-Differential Operators on S?/sup>?/sub>(Rd)	p. 256
  A Short Survey on Travelling Waves	p. 271
  Semilinear G-Equations	p. 275
  Notes	p. 285
  Bibliography	p. 287
  Index	p. 301
  Index of Notation	p. 305
  Table of Contents provided by Ingram. All Rights Reserved.

기본정보

ISBN	9783764385118 ( 3764385111 )
발행(출시)일자	2010년 05월 31일
쪽수	306쪽
크기	168 * 236 * 18 mm / 612 g
총권수	1권
언어	영어