Classical Microlocal Analysis in the Space of Hyperfunctions

Seiichiro Wakabayashi (eds.)3540676031, 9783540676034

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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Table of contents :
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