An introduction to semiclassical and microlocal analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2002
|
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 190 S. |
| ISBN: | 0387953442 9780387953441 |
Internformat
MARC
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| 245 | 1 | 0 | |a An introduction to semiclassical and microlocal analysis |c André Martinez |
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| 650 | 4 | |a Théorie quantique | |
| 650 | 4 | |a Quantentheorie | |
| 650 | 4 | |a Microlocal analysis | |
| 650 | 4 | |a Quantum theory | |
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Datensatz im Suchindex
| _version_ | 1804129033444655104 |
|---|---|
| adam_text | Contents
Preface v
1 Introduction 1
1.1 A Short Review of Classical Mechanics 1
1.2 Basic Notions of Quantum Mechanics 3
1.3 Semiclassical Analysis 7
1.4 About History 8
2 Semiclassical Pseudodifferential Calculus 9
2.1 Motivation and Notation 9
2.2 Spaces of Symbols 10
2.3 Semiclassical Expansions of Symbols 13
2.4 Oscillatory Integrals 17
2.5 Pseudodifferential Operators 22
2.6 Composition 27
2.7 Change of Quantization Symbolic Calculus 36
2.8 L2 Continuity 43
2.9 A First Application: The Frequency Set 51
2.10 Exercises and Problems 55
3 Microlocalization 69
3.1 The Global FBI Transform 69
3.2 Microsupport 73
3.3 Action of the FBI Transform on #DOs 77
3.4 Action of the FBI Transform on FIOs 79
3.5 Microlocal Exponential Estimates 87
3.6 Exercises and Problems 96
vii
viii CONTENTS
4 Applications to the Solutions of Analytic Linear PDEs 105
4.1 Projection of the Microsupport 105
4.2 Characteristic Set and Microsupport Ill
4.3 Propagation of the Microsupport 114
4.4 Microhyperbolicity 125
4.5 Boundary Value Problems 130
4.6 Exercises and Problems 132
5 Complements: Symplectic Aspects 141
5.1 The Canonical Symplectic Form on R2n 141
5.2 Symplectic Transformations 142
5.3 Hamilton Field 144
5.4 Lagrangian Submanifolds 146
5.5 Applications to the Study of PDEs 147
5.6 Exercises and Problems 161
6 Appendix: List of Formulae 169
6.1 Change of Quantization 169
6.1.1 Semiclassical Calculus 169
6.1.2 Nonsemiclassical Calculus 170
6.2 Composition Formulae 170
6.2.1 Semiclassical Calculus 170
6.2.2 Nonsemiclassical Calculus 170
6.3 Symbol of the Adjoint and Transpose Operator 171
6.3.1 Semiclassical Calculus 171
6.3.2 Nonsemiclassical Calculus 172
6.4 Symbol of a Commutator 172
6.5 Functional Calculus 172
6.6 Fourier Bros Iagolnitzer Transform 172
6.7 Microlocal Exponential Estimates 173
6.8 Agmon Estimates 173
Bibliography 175
Index 183
List of Notation 189
|
| any_adam_object | 1 |
| author | Martinez, André |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.15/57242 |
| dewey-search | 530.15/57242 |
| dewey-sort | 3530.15 557242 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:58:42Z |
| institution | BVB |
| isbn | 0387953442 9780387953441 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009703691 |
| oclc_num | 47667235 |
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| physical | VIII, 190 S. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
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| publisher | Springer |
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| series2 | Universitext |
| spelling | Martinez, André (DE-588)1151889792 aut An introduction to semiclassical and microlocal analysis André Martinez New York [u.a.] Springer 2002 VIII, 190 S. txt rdacontent n rdamedia nc rdacarrier Universitext Analyse microlocale Lokale analyse (wiskunde) gtt Théorie quantique Quantentheorie Microlocal analysis Quantum theory Quantentheorie (DE-588)4047992-4 gnd rswk-swf Quasiklassische Näherung (DE-588)4296820-3 gnd rswk-swf Mikrolokale Analysis (DE-588)4169832-0 gnd rswk-swf Quantentheorie (DE-588)4047992-4 s Quasiklassische Näherung (DE-588)4296820-3 s Mikrolokale Analysis (DE-588)4169832-0 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4757-4495-8 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009703691&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Martinez, André An introduction to semiclassical and microlocal analysis Analyse microlocale Lokale analyse (wiskunde) gtt Théorie quantique Quantentheorie Microlocal analysis Quantum theory Quantentheorie (DE-588)4047992-4 gnd Quasiklassische Näherung (DE-588)4296820-3 gnd Mikrolokale Analysis (DE-588)4169832-0 gnd |
| subject_GND | (DE-588)4047992-4 (DE-588)4296820-3 (DE-588)4169832-0 |
| title | An introduction to semiclassical and microlocal analysis |
| title_auth | An introduction to semiclassical and microlocal analysis |
| title_exact_search | An introduction to semiclassical and microlocal analysis |
| title_full | An introduction to semiclassical and microlocal analysis André Martinez |
| title_fullStr | An introduction to semiclassical and microlocal analysis André Martinez |
| title_full_unstemmed | An introduction to semiclassical and microlocal analysis André Martinez |
| title_short | An introduction to semiclassical and microlocal analysis |
| title_sort | an introduction to semiclassical and microlocal analysis |
| topic | Analyse microlocale Lokale analyse (wiskunde) gtt Théorie quantique Quantentheorie Microlocal analysis Quantum theory Quantentheorie (DE-588)4047992-4 gnd Quasiklassische Näherung (DE-588)4296820-3 gnd Mikrolokale Analysis (DE-588)4169832-0 gnd |
| topic_facet | Analyse microlocale Lokale analyse (wiskunde) Théorie quantique Quantentheorie Microlocal analysis Quantum theory Quasiklassische Näherung Mikrolokale Analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009703691&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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