An Introduction to Pseudo-Differential Operators

The aim of this third edition is to give an accessible and essentially self-contained account of pseudo-differential operators based on the previous edition. New chapters notwithstanding, the elementary and detailed style of earlier editions is maintained in order to appeal to the largest possible group of readers. The focus of this book is on the global theory of elliptic pseudo-differential operators on Lp(Rn).

The main prerequisite for a complete understanding of the book is a basic course in functional analysis up to the level of compact operators. It is an ideal introduction for graduate students in mathematics and mathematicians who aspire to do research in pseudo-differential operators and related topics.
Contents:Introduction, Notation and PreliminariesDifferentiation of Integrals Depending on ParametersThe ConvolutionThe Fourier TransformTempered DistributionsSymbols, Pseudo-Differential Operators and Asymptotic ExpansionsA Partition of Unity and Taylor's FormulaThe Product of Two Pseudo-Differential OperatorsThe Formal Adjoint of a Pseudo-Differential OperatorThe Parametrix of an Elliptic Pseudo-Differential OperatorLp-Boundedness of Pseudo-Differential OperatorsThe Sobolev Spaces Hs,p, -∞<s<∞, 1≤p<∞Closed Linear OperatorsMinimal and Maximal Pseudo-Differential OperatorsGlobal Regularity of Elliptic Partial Differential EquationsWeak Solutions of Pseudo-Differential EquationsGårding's InequalityStrong Solutions of Pseudo-Differential EquationsOne-Parameter Semigroups Generated by Pseudo-Differential OperatorsFredholm OperatorsFredholm Pseudo-Differential OperatorsSymmetrically Global Pseudo-Differential OperatorsSpectral Invariance of Symmetrically Global Pseudo-Differential Operators
Readership: Graduate students and researchers in the fields of analysis and differential equations.
Key Features:The existing books on pseudo-differential operators serve well as references, but are not suitable as textbooks. They are too difficult for students to learn the basics in order to do research in the field expeditiouslyThe third edition of this book contains new topics that give a much better perspective of the global theory of elliptic pseudo-differential operators than the earlier editionsWhile the topics in the competing book by M A Shubin are mainly given in the context of L2(Rn), a unique feature of this book is that the emphasis has been put on the theory of pseudo-differential operators on Lp(Rn), where p is between 1 and infinity/li>