Pseudo-differential operators and the Nash-Moser theorem
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Bibliographic Information
Pseudo-differential operators and the Nash-Moser theorem
（Graduate studies in mathematics, v. 82）
American Mathematical Society, c2007
- Other Title
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Opérateurs pseudo-différentiels et théorème de Nash-Moser
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Translation of: Opérateurs pseudo-différentiels et théorème de Nash-Moser
Includes bibliographical references (p. 161-163) and index
Description and Table of Contents
Description
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.
Table of Contents
General introduction Notation and review of distribution theory Pseudo-differential operators Nonlinear dyadic analysis, microlocal analysis, energy estimates Implicit function theorems Bibliography Main notation introduced Index.
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