An Introduction to Microlocal Analysis
Series: Graduate Texts in Mathematics; 304;
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Product details:
- Publisher Springer Nature Switzerland
- Date of Publication 26 September 2025
- Number of Volumes 1 pieces, Book
- ISBN 9783031907050
- Binding Hardback
- No. of pages373 pages
- Size 235x155 mm
- Language English
- Illustrations XV, 373 p. 35 illus., 22 illus. in color. Illustrations, black & white 700
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Long description:
"
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.
" MoreTable of 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.
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