Translated by Stephen S. Wilson
Hardcover ISBN:  9780821834541 
Product Code:  GSM/82 
List Price:  $99.00 
MAA Member Price:  $89.10 
AMS Member Price:  $79.20 
eBook ISBN:  9781470421120 
Product Code:  GSM/82.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Hardcover ISBN:  9780821834541 
eBook: ISBN:  9781470421120 
Product Code:  GSM/82.B 
List Price:  $184.00 $141.50 
MAA Member Price:  $165.60 $127.35 
AMS Member Price:  $147.20 $113.20 
Translated by Stephen S. Wilson
Hardcover ISBN:  9780821834541 
Product Code:  GSM/82 
List Price:  $99.00 
MAA Member Price:  $89.10 
AMS Member Price:  $79.20 
eBook ISBN:  9781470421120 
Product Code:  GSM/82.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Hardcover ISBN:  9780821834541 
eBook ISBN:  9781470421120 
Product Code:  GSM/82.B 
List Price:  $184.00 $141.50 
MAA Member Price:  $165.60 $127.35 
AMS Member Price:  $147.20 $113.20 

Book DetailsGraduate Studies in MathematicsVolume: 82; 2007; 168 ppMSC: Primary 35; Secondary 47
This book presents two essential and apparently unrelated subjects. The first, microlocal analysis and the theory of pseudodifferential 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 selfcontained 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.
ReadershipGraduate students and research mathematicians interested in microlocal analysis, PDE, and geometry.

Table of Contents

Chapters

General introduction

Chapter 0. Notation and review of distribution theory

Chapter I. Pseudodifferential operators

Chapter II. Nonlinear dyadic analysis, microlocal analysis, energy estimates

Chapter III. Implicit function theorems


Additional Material

Reviews

The authors made a great accomplishment in writing this beautiful and elegant text, of great value to both students and researchers.
Zentralblatt MATH


RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Additional Material
 Reviews
 Requests
This book presents two essential and apparently unrelated subjects. The first, microlocal analysis and the theory of pseudodifferential 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 selfcontained 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.
Graduate students and research mathematicians interested in microlocal analysis, PDE, and geometry.

Chapters

General introduction

Chapter 0. Notation and review of distribution theory

Chapter I. Pseudodifferential operators

Chapter II. Nonlinear dyadic analysis, microlocal analysis, energy estimates

Chapter III. Implicit function theorems

The authors made a great accomplishment in writing this beautiful and elegant text, of great value to both students and researchers.
Zentralblatt MATH