Pseudo-differential Operators and the Nash-Moser Theorem

This book presents two essential and apparently unrelated subjects. The first, microlocal analysis and the theory of pseudo-differential operators, is a basic tool in the study of partial differential equations and in analysis on manifolds. The second, the Nash-Moser theorem, continues to be fundamentally important in geometry, dynamical systems and nonlinear PDE. Each of the subjects, which are of interest in their own right as well as for applications, can be learned separately. But the book shows the deep connections between the two themes, particularly in the middle part, which is devoted to Littlewood-Paley theory, dyadic analysis, and the paradifferential calculus and its application to interpolation inequalities. An important feature is the elementary and self-contained character of the text, to which many exercises and an introductory Chapter $0$ with basic material have been added. This makes the book readable by graduate students or researchers from one subject who are interested in becoming familiar with the other. It can also be used as a textbook for a graduate course on nonlinear PDE or geometry.

ISBN 0821834541   DEWEY edition DC22 ISBN13 9780821834541 (What's this?)   Pages 168 Publisher American Mathematical Society   Volumes 001 Imprint American Mathematical Society   Weight (grammes) 468 Format Hardback   Published in Providence Publication date 15 Apr 2007   Series title Graduate Studies in Mathematics Library of Congress QA329.7   Spine width (mm) 14 DEWEY 515.35   Academic level Professional / Scholarly

		Notation and review of distribution theory		5
Ch. I		Pseudo-differential operators		15
Ch. II		Nonlinear dyadic analysis, microlocal analysis, energy estimates		77
Ch. III		Implicit function theorems		121

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