Classical Microlocal Analysis in the Space of Hyperfunctions

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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.

Author(s): Seiichiro Wakabayashi (eds.)
Series: Lecture Notes in Mathematics 1737
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2000

Language: English
Pages: 370
City: Berlin; New York
Tags: Analysis; Partial Differential Equations

Hyperfunctions....Pages 5-39
Basic calculus of fourier integral operators and pseudodifferential operators....Pages 41-114
Analytic wave front sets and microfunctions....Pages 115-204
Microlocal uniqueness....Pages 205-258
Local solvability....Pages 259-293