The book develops "Classical Microlocal Analysis" in the spaces of hyperfunctions and microfunctions, which makes it possible to apply the methods in the distribution category to the studies on partial differential equations in the hyperfunction category. Here "Classical Microlocal Analysis" means that it does not use "Algebraic Analysis." The main tool in the text is, in some sense, integration by parts. The studies on microlocal uniqueness, analytic hypoellipticity and local solvability are reduced to the problems to derive energy estimates (or a priori estimates). The author assumes basic understanding of theory of pseudodifferential operators in the distribution category.

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“This book will be very useful to everyone who wishes to work in the area of analytic coefficient partial differential equations by using methods from the usual distribution theory.” (Alberto Parmeggiani, zbMATH 0949.35003, 2022)

Bibliographic Information

Book Title: Classical Microlocal Analysis in the Space of Hyperfunctions
Editors: Seiichiro Wakabayashi
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/BFb0103767
Publisher: Springer Berlin, Heidelberg
eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 2000
Softcover ISBN: 978-3-540-67603-4Published: 23 June 2000
eBook ISBN: 978-3-540-45161-7Published: 06 May 2007
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: X, 370
Topics: Analysis, Partial Differential Equations

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Table of contents (5 chapters)

Front Matter

Hyperfunctions

Basic calculus of fourier integral operators and pseudodifferential operators

Analytic wave front sets and microfunctions

Microlocal uniqueness

Local solvability

Back Matter

About this book