D-modules and microlocal calculus:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English Japanese |
| Veröffentlicht: |
Providence, R.I.
American Mathematical Society
2003
|
| Schriftenreihe: | Translations of mathematical monographs
217 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XVI, 254 S. |
| ISBN: | 0821827669 |
Internformat
MARC
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| 240 | 1 | 0 | |a Dais¯u kaiseki gairon |
| 245 | 1 | 0 | |a D-modules and microlocal calculus |c Masaki Kashiwara. Transl. [from the Japanese] by Mutsumi Saito |
| 264 | 1 | |a Providence, R.I. |b American Mathematical Society |c 2003 | |
| 300 | |a XVI, 254 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Translations of mathematical monographs |v 217 | |
| 490 | 0 | |a Iwanami series in modern mathematics | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Analyse microlocale | |
| 650 | 4 | |a D-modules, Théorie des | |
| 650 | 4 | |a D-modules | |
| 650 | 4 | |a Microlocal analysis | |
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Datensatz im Suchindex
| _version_ | 1804133124217503744 |
|---|---|
| adam_text | Contents
Preface ix
Preface to the English Edition xi
Introduction xiii
Chapter 1. Basic Properties of D modules 1
1.1. D modules 1
1.2. Differential Homomorphisms of Ox mod iles 2
1.3. A System of Generators of D 6
1.4. Left Z x modules and Right Px modules 7
Chapter 2. Characteristic Varieties 11
2.1. Cotangent Bundles 11
2.2. Characteristic Varieties 15
2.3. Involutivity 21
2.4. Codimension Filtration 22
Chapter 3. Construction of D modules 29
3.1. Tensor Products 29
3.2. Homological Properties of D modules 32
3.3. Dual Module 36
3.4. Algebraic Relative Cohomology 39
Chapter 4. Functorial Properties of D modules 57
4.1. Pull backs of D modules 57
4.2. Derived Functors of Inverse Images 59
4.3. External Tensor Product 60
4.4. Coherence of Inverse Images 61
4.5. Cauchy Kovalevskaya Theorem 68
4.6. Integrals of D modules 74
4.7. Coherence of Integrals 76
V
vi CONTENTS
4.8. £ modules Supported by a Submanifold 84
4.9. Adjunction Formula 87
4.10. Adjunction Formula (Inverse Form) 93
4.11. Holonomic Systems 94
Chapter 5. Regular Holonomic Systems 99
5.1. Ordinary Differential Equations
with Regular Singularities 99
5.2. Holonomic Modules with Regular Singularities 100
5.3. Riemann Hilbert Correspondence 102
Chapter 6. 6 functions 105
6.1. Motivation for 6 functions 105
6.2. £ module Generated by f(x)s 106
6.3. Rationality of 6 functions 109
6.4. 6 functions in the Case of
Quasi homogeneous Isolated Singularities 114
6.5. fc function and Irreducibility 117
Chapter 7. Ring of Formal Microdifferential Operators 123
7.1. Microlocalization 123
7.2. Formal MicrodifFerential Operators on Manifolds 125
7.3. Microdifferential Operators 129
7.4. Algebraic Properties of £ 130
7.5. Relations between T x and £x 139
7.6. Involutivity of the Supports of Coherent ^ modules 147
Chapter 8. Microlocal Analysis of Holonomic Systems 153
8.1. Simple f modules 153
8.2. Quantized Contact Transformation 153
8.3. Subprincipal Symbols 159
8.4. Preparation for the Classification
of Simple Holonomic Systems 161
8.5. Classification of Simple Holonomic Systems (1) 168
8.6. Principal Symbols of Simple Holonomic Modules 170
8.7. Regular Holonomic £x modules 176
8.8. Classification of Simple Holonomic Systems (2) 181
8.9. Subholonomic Systems 186
Chapter 9. Microlocal Calculus of 6 functions 191
9.1. Microlocal 6 functions 191
CONTENTS vii
9.2. Existence of Microlocal b functions 196
9.3. Simple Intersection of Lagrangian Analytic Subsets 200
9.4. Relation of 6 functions of Two Lagrangian
Analytic Subsets with a Good Intersection 201
9.5. 6 functions of Relative Invariants 205
Appendix 213
A.I. Finiteness of Filtered Rings and Their Modules 213
A.2. Derived Categories 226
A.3. Derived Functors on Categories of Modules 239
A.4. Symplectic Manifolds 243
Bibliography 247
Index 251
Index of Notations 253
|
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| dewey-raw | 516.3/6 |
| dewey-search | 516.3/6 |
| dewey-sort | 3516.3 16 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV019683038 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T20:03:43Z |
| institution | BVB |
| isbn | 0821827669 |
| language | English Japanese |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013010981 |
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| physical | XVI, 254 S. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs Iwanami series in modern mathematics |
| spelling | Kashiwara, Masaki 1947- Verfasser (DE-588)122204344 aut Dais¯u kaiseki gairon D-modules and microlocal calculus Masaki Kashiwara. Transl. [from the Japanese] by Mutsumi Saito Providence, R.I. American Mathematical Society 2003 XVI, 254 S. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 217 Iwanami series in modern mathematics Includes bibliographical references and index Analyse microlocale D-modules, Théorie des D-modules Microlocal analysis Mikrolokale Analysis (DE-588)4169832-0 gnd rswk-swf D-Modul (DE-588)4305548-5 gnd rswk-swf D-Modul (DE-588)4305548-5 s DE-604 Mikrolokale Analysis (DE-588)4169832-0 s Translations of mathematical monographs 217 (DE-604)BV000002394 217 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013010981&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kashiwara, Masaki 1947- D-modules and microlocal calculus Translations of mathematical monographs Analyse microlocale D-modules, Théorie des D-modules Microlocal analysis Mikrolokale Analysis (DE-588)4169832-0 gnd D-Modul (DE-588)4305548-5 gnd |
| subject_GND | (DE-588)4169832-0 (DE-588)4305548-5 |
| title | D-modules and microlocal calculus |
| title_alt | Dais¯u kaiseki gairon |
| title_auth | D-modules and microlocal calculus |
| title_exact_search | D-modules and microlocal calculus |
| title_full | D-modules and microlocal calculus Masaki Kashiwara. Transl. [from the Japanese] by Mutsumi Saito |
| title_fullStr | D-modules and microlocal calculus Masaki Kashiwara. Transl. [from the Japanese] by Mutsumi Saito |
| title_full_unstemmed | D-modules and microlocal calculus Masaki Kashiwara. Transl. [from the Japanese] by Mutsumi Saito |
| title_short | D-modules and microlocal calculus |
| title_sort | d modules and microlocal calculus |
| topic | Analyse microlocale D-modules, Théorie des D-modules Microlocal analysis Mikrolokale Analysis (DE-588)4169832-0 gnd D-Modul (DE-588)4305548-5 gnd |
| topic_facet | Analyse microlocale D-modules, Théorie des D-modules Microlocal analysis Mikrolokale Analysis D-Modul |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013010981&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000002394 |
| work_keys_str_mv | AT kashiwaramasaki daisukaisekigairon AT kashiwaramasaki dmodulesandmicrolocalcalculus |