Pseudo-differential Operators and the Nash-Moser Theorem

Alinhac, Serge; Gerard, Patrick

ISBN 10: 0821834541 / ISBN 13: 9780821834541

Published by Amer Mathematical Society, 2007

About this Item

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Bibliographic Details

• Title: Pseudo-differential Operators and the Nash-Moser Theorem
• Publisher: Amer Mathematical Society
• Publication Date: 2007
• Language: English
• ISBN 10: 0821834541
• ISBN 13: 9780821834541
• Binding: Hardcover
• Condition: good

About this title

Synopsis

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.