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An introduction to microlocal analysis

Record Type:	Electronic resources : Monograph/item
Title/Author:	An introduction to microlocal analysis/ by Peter Hintz.
Author:	Hintz, Peter.
Published:	Cham :Springer Nature Switzerland : : 2025.,
Description:	xv, 373 p. :ill. (some col.), digital ;24 cm.
[NT 15003449]:	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.
Contained By:	Springer Nature eBook
Subject:	Differential equations, Linear. -
Online resource:	https://doi.org/10.1007/978-3-031-90706-7
ISBN:	9783031907067

An introduction to microlocal analysis
Hintz, Peter.

An introduction to microlocal analysis[electronic resource] /by Peter Hintz. - Cham :Springer Nature Switzerland :2025. - xv, 373 p. :ill. (some col.), digital ;24 cm. - Graduate texts in mathematics,3042197-5612 ;. - Graduate texts in mathematics ;304..

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.

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.

ISBN: 9783031907067

Standard No.: 10.1007/978-3-031-90706-7doiSubjects--Topical Terms:

708540
Differential equations, Linear.

LC Class. No.: QA372

Dewey Class. No.: 515.354

An introduction to microlocal analysis
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490 1 $a Graduate texts in mathematics, $x 2197-5612 ; $v 304
505 0 $a 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.
520 $a 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.
650 0 $a Differential equations, Linear. $3 708540
650 0 $a Differential equations, Partial. $3 518115
650 0 $a Pseudodifferential operators. $3 579200
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950 $a Mathematics and Statistics (SpringerNature-11649)