An Introduction to Pseudo-Differential Operators

by Wong, Man Wah

• ISBN13: 9789810238131
• ISBN10: 9810238134
• Edition: 2nd
• Format: Hardcover
• Copyright: 1999-02-01
• Publisher: WORLD SCIENTIFIC PUB CO INC

Summary

In this new edition of An Introduction to Pseudo Differential Operators, the style and scope of the original book are retained. A chapter on the interchange of order of differentiation and integration is added at the beginning to make the book more self-contained, and a chapter on weak solutions of pseudo-differential equations is added at the end to enhance the value of the book as a work on partial differential equations. Several chapters are provided with additional exercises. The bibliography is slightly expanded and an index is added.

Table of Contents

Preface for the Second Edition	v
Preface	vii
Introduction, Notation and Preliminaries	1	(4)
Differentiation of Integrals Depending on Parameters	5	(4)
The Convolution	9	(8)
The Fourier Transform	17	(12)
Tempered Distributions	29	(6)
Symbols, Pseudo-Differential Operators and Asymptotic Expansions	35	(14)
A Partition of Unity and Taylor's Formula	49	(14)
The Product of Two Pseudo-Differential Operators	63	(8)
The Formal Adjoint of a Pseudo-Differential Operator	71	(10)
The Parametrix of an Elliptic Pseudo-Differential Operator	81	(8)
Lp-Boundedness of Pseudo-Differential Operators	89	(14)
The Sobolev Spaces Hs,p, -∞ < s < ∞, 1 ≤ p < ∞	103	(10)
Closed Linear Operators	113	(6)
Minimal and Maximal Pseudo-Differential Operators	119	(8)
Global Regularity of Elliptic Partial Differential Equations	127	(4)
Weak Solutions of Pseudo-Differential Equations	131	(4)
Bibliography	135	(2)
Index	137