Classical Microlocal Analysis in the Space of Hyperfunctions

• Main Author: Wakabayashi, Seiichiro (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2000.
• Edition: 1st ed. 2000.
• Series: Lecture Notes in Mathematics, 1737
• Subjects: Mathematical analysis.; Analysis (Mathematics).; Partial differential equations.; Analysis.; Partial Differential Equations.
• Physical Description: X, 370 p. online resource.
• ISBN: 9783540451617
• ISSN: 0075-8434 ;
• DOI: 10.1007/BFb0103767

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.