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Classical Microlocal Analysis in the Space of Hyperfunctions : Lecture Notes in Mathematics - Seiichiro Wakabayashi

Classical Microlocal Analysis in the Space of Hyperfunctions

Lecture Notes in Mathematics

Paperback Published: July 2000
ISBN: 9783540676034
Number Of Pages: 370

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The book develops "Classical Microlocal Analysis" in the spaces of hyperfunctions & 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 & 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.

Hyperfunctionsp. 5
Function spaces?p. 5
Supportsp. 13
Localizationp. 23
Hyperfunctionsp. 28
Further applications of the Runge approximation theoremp. 34
Basic calculus of Fourier integral operators and pseudo-diferential operatorsp. 41
Preliminary lemmasp. 41
Symbol classesp. 52
Definition of Fouier integral operatorsp. 57
Product formula of Fourier integral operators Ip. 65
Product formula of Fourier integral operators IIp. 87
Pseudolocal propertiesp. 93
Pseudodifferential operators in ßp. 107
Parametrices of elliptic operatorsp. 112
Analytic wave ront sets and micro functionsp. 115
Analytic wave front setsp. 115
Action of Fourier integral operators on wave front setsp. 130
The boundary values of analytic functionsp. 155
Operations on hyperfunctionsp. 165
Hyperfunctions supported by a half-spacep. 183
Microfunctionsp. 192
Formal analytic symbolsp. 201
Microlocal uniquenessp. 205
Preliminary lemmasp. 205
General resultsp. 222
Microhyperbolic operatorsp. 231
Canonical transformationp. 239
Hypoellipticityp. 244
Local solvabilityp. 259
Preliminariesp. 259
Necessary conditions on local solvability and hypoellipticity 268
Sufficient conditions on local solvabilityp. 272
Some examplesp. 285
A Proofs of product formulaep. 295
Proof of Theorem 2.4.4p. 295
Proof of Corollary 2.4.5p. 323
Proof of Theorem 2.4.6p. 328
Proof of Corollary 2.4.7p. 336
Proof of Theorem 2.5.3p. 338
A priori estimatesp. 351
Grusin operatorsp. 351
A class of operators with double characteristicsp. 355
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9783540676034
ISBN-10: 3540676031
Series: Lecture Notes in Mathematics
Audience: General
Format: Paperback
Language: English
Number Of Pages: 370
Published: July 2000
Publisher: SPRINGER VERLAG GMBH
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 1.98
Weight (kg): 0.53

Earn 232 Qantas Points
on this Book