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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.
| Hyperfunctions | p. 5 |
| Function spaces? | p. 5 |
| Supports | p. 13 |
| Localization | p. 23 |
| Hyperfunctions | p. 28 |
| Further applications of the Runge approximation theorem | p. 34 |
| Basic calculus of Fourier integral operators and pseudo-diferential operators | p. 41 |
| Preliminary lemmas | p. 41 |
| Symbol classes | p. 52 |
| Definition of Fouier integral operators | p. 57 |
| Product formula of Fourier integral operators I | p. 65 |
| Product formula of Fourier integral operators II | p. 87 |
| Pseudolocal properties | p. 93 |
| Pseudodifferential operators in ß | p. 107 |
| Parametrices of elliptic operators | p. 112 |
| Analytic wave ront sets and micro functions | p. 115 |
| Analytic wave front sets | p. 115 |
| Action of Fourier integral operators on wave front sets | p. 130 |
| The boundary values of analytic functions | p. 155 |
| Operations on hyperfunctions | p. 165 |
| Hyperfunctions supported by a half-space | p. 183 |
| Microfunctions | p. 192 |
| Formal analytic symbols | p. 201 |
| Microlocal uniqueness | p. 205 |
| Preliminary lemmas | p. 205 |
| General results | p. 222 |
| Microhyperbolic operators | p. 231 |
| Canonical transformation | p. 239 |
| Hypoellipticity | p. 244 |
| Local solvability | p. 259 |
| Preliminaries | p. 259 |
| Necessary conditions on local solvability and hypoellipticity 268 | |
| Sufficient conditions on local solvability | p. 272 |
| Some examples | p. 285 |
| A Proofs of product formulae | p. 295 |
| Proof of Theorem 2.4.4 | p. 295 |
| Proof of Corollary 2.4.5 | p. 323 |
| Proof of Theorem 2.4.6 | p. 328 |
| Proof of Corollary 2.4.7 | p. 336 |
| Proof of Theorem 2.5.3 | p. 338 |
| A priori estimates | p. 351 |
| Grusin operators | p. 351 |
| A class of operators with double characteristics | p. 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
