文档介绍：Contents
Preface ix
Introduction 1
Background material 9
....................... 9
............... 11
Identities and Inequalities for Factorials and Binomial Coefficients 13
1 Global Pseudo-Differential Calculus 15
Summary................................... 15
............................. 19
............................. 23
Action on S ........................... 23
Adjoint and Transposed Operator. Action on S ....... 29
................... 31
............................ 34
Hypoellipticity and Construction of the Parametrix . . . . . 35
Slow Variation and Construction of Elliptic Symbols . . . . 38
Boundedness on L2 ........................... 40
............................. 41
.......................... 45
AbstractTheory........................ 46
Pseudo-DifferentialOperators................. 50
-WickQuantization........................ 51
Short-Time Fourier Transform and Anti-Wick Operators . . 52
RelationshipwiththeWeylQuantization.......... 54
Applications to Boundedness on L2 and Almost Positivity
ofPseudo-DifferentialOperators............... 58
SobolevSpacesRevisited................... 60
................ 62
Notes..................................... 64
vi Contents
2 Γ-Pseudo-Differential Operators and H-Polynomials 67
Summary................................... 67
Γ-Pseudo-DifferentialOperators.................... 70
Γ-Elliptic Differential Operators; the Harmonic Oscillator . . . . . 77
Asymptotic Integration and Solutions of Exponential Type . . . . 82
-Polynomials............................. 88
-EllipticPolynomials....................... 94
-Quasi-EllipticPolynomials................... 97