An Introduction to Microlocal Analysis / by Peter Hintz.

Format:

Book

Author/Creator:

Hintz, Peter.

Series:

Graduate Texts in Mathematics, 2197-5612 ; 304

Language:

English

Subjects (All):

Differential equations.

Dynamics.

Differential Equations.

Dynamical Systems.

Local Subjects:

Differential Equations.

Dynamical Systems.

Physical Description:

1 online resource (801 pages)

Edition:

1st ed. 2025.

Place of Publication:

Cham : Springer Nature Switzerland : Imprint: Springer, 2025.

Summary:

Microlocal analysis provides a powerful, versatile, and modular perspective on the analysis of linear partial differential equations. This text, developed from a first-year graduate course, provides an accessible introduction and develops, from first principles, the core notions and results including pseudodifferential operators, wave front sets, and propagation phenomena. The reader is assumed to have some exposure to functional analysis and the theory of smooth manifolds. With detailed proofs, a wealth of exercises of varying levels of difficulty, and connections to contemporary research in general relativity, the book serves as both a comprehensive textbook for graduate students and a useful reference for researchers.

Contents:

Preface

1. Introduction

2. Schwartz functions and tempered distributions

3. Symbols

4. Pseudodifferential operators

5. Pseudodifferential operators on manifolds

6. Microlocalization

7. Hyperbolic evolution equations and Egorov's theorem

8. Real principal type propagation of singularities

9. Solving wave-type equations

10. Propagation of singularities at radial sets

11. Late time asymptotics of linear waves on de Sitter space

Bibliography

Index.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

9783031907067

3-031-90706-X

OCLC:

1553069831