Microdifferential systems in the complex domain:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin u.a.
Springer
1985
|
| Series: | Grundlehren der mathematischen Wissenschaften
269 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 214 S. |
| ISBN: | 354013672X 038713672X |
Staff View
MARC
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| 245 | 1 | 0 | |a Microdifferential systems in the complex domain |c Pierre Schapira |
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Record in the Search Index
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| adam_text | Contents
Introduction 1
Chapter I. Microdifferential Operators 5
Summary 5
§ 1. Construction of the Ring 9x 6
1.1. Differential Operators 6
1.2. Formal Microdifferential Operators 9
1.3. Microdifferential Operators 11
Exercises 13
§ 2. Division Theorems 14
2.1. A Banach Algebra of Operators 14
2.2. The Spath and Weierstrass Theorems 16
Exercises 19
§3. Refined Microdifferential Cauchy Kowalewski Theorem .... 20
3.1. Statement of the Theorem 20
3.2. The Abstract Cauchy Kowalewski Theorem in Scales of Banach
Spaces 22
3.3. Proof of Theorem 3.1.1 24
Exercises 25
§ 4. Microdifferential Modules Associated to a Submanifold 26
4.1. The Sheaf ^ZIV 26
4.2. The Case when Z is a Hypersurface 30
4.3. The Sheaf WY^X 32
Exercises 33
§ 5. Quantized Contact Transformations 34
5.1. Division by an Ideal 34
5.2. Adjoint 36
5.3. Quantized Contact Transformations 37
5.4. Examples 39
Exercises 41
VIII Contents
§ 6. Systems with Simple Characteristics 43
6.1. Equivalence of Operators 43
6.2. The Regular Involutive Case 44
6.3. Holonomic Systems with Simple Characteristics 46
Exercises 47
Notes 48
Chapter II. Wx modules 50
Summary 50
§1. Filtered Rings and Modules 51
1.1. Noetherian and Zariskian Filtrations 51
1.2. Homological Properties 58
1.3. Characteristic Ideal 61
1.4. Sheaves of Filtered Modules 65
1.5. Examples 69
Exercises 71
§ 2. Structure of the Ring %x 72
2.1. The Ring g^O) 72
2.2. Main Properties of Wx 76
2.3. Characteristic Cycle 79
2.4. Holonomic Modules 81
2.5. Adjunction of a Dummy Variable 84
2.6. .S^ modules 86
Exercises 88
§3. Operations on l^ modules 90
3.1. Definitions 90
3.2. Operations on Ssyx 94
3.3. Operations on c^sxx 99
3.4. Operations on ^ modules 102
3.5. Complement on Inverse Images 108
Exercises Ill
Notes 112
Chapter III. Cauchy Problem and Propagation 114
Summary 114
§1. Microcharacteristic Varieties 116
1.1. Normal Cones 116
1.2. 1 microcharacteristic Variety 119
1.3. Characteristic Varieties Associated to a Submersion 124
1.4. Characteristic Varieties Associated to an Embedding 127
1.5. Characteristic Variety of the Systems Induced on a Submanifold 130
Contents IX
1.6. Coherency of the Systems Induced on a Submanifold 133
Exercises 136
§2. The Cauchy Problem 137
2.1. The Cauchy Problem for a System 137
2.2. Application: The Cauchy Problem with Data Ramified along
Hypersurfaces 143
Exercises 147
§3. Propagation 148
3.1. Propagation at the Boundary for one Operator 148
3.2. Propagation for Systems 155
Exercises 157
§4. Constructibility 158
4.1. Real and Complex Stratifications 158
4.2. Micro support of Sheaves 163
4.3. Micro supports and Microcharacteristic Varieties 165
Exercises 169
Notes 171
Appendices 173
A. Symplectic Geometry 173
A.l. Symplectic Vector Spaces 173
A.2. Symplectic Manifolds 174
A.3. Homogeneous Symplectic Structures 175
A.4. Contact Transformations 176
B. Homological Algebra 179
B.I. Categories and Derived Functors 179
B.2. Rings and Modules 184
B.3. Graded Rings and Modules 186
B.4. Koszul Complexes 187
B.5. The Mittag Leffler Condition 189
C. Sheaves 190
C.I. Presheaves and Sheaves 190
C.2. Cohomology of Sheaves 192
C.3. Cech Cohomology 194
C.4. An Extension Theorem 195
C.5. Coherent Sheaves 198
D. ^ modules 199
D.I. Support and Multiplicities 199
D.2. Homological Dimension 202
X Contents
Bibliography 203
List of Notations and Conventions 207
Index 212
|
| any_adam_object | 1 |
| author | Schapira, Pierre 1943- |
| author_GND | (DE-588)10785130X |
| author_facet | Schapira, Pierre 1943- |
| author_role | aut |
| author_sort | Schapira, Pierre 1943- |
| author_variant | p s ps |
| building | Verbundindex |
| bvnumber | BV000253147 |
| classification_rvk | SK 240 SK 500 SK 540 SK 620 |
| classification_tum | MAT 322f MAT 474f |
| ctrlnum | (OCoLC)246634232 (DE-599)BVBBV000253147 |
| dewey-full | 515.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.353 |
| dewey-search | 515.353 |
| dewey-sort | 3515.353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| institution | BVB |
| isbn | 354013672X 038713672X |
| language | English |
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| physical | X, 214 S. |
| publishDate | 1985 |
| publishDateSearch | 1985 |
| publishDateSort | 1985 |
| publisher | Springer |
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| series | Grundlehren der mathematischen Wissenschaften |
| series2 | Grundlehren der mathematischen Wissenschaften |
| spelling | Schapira, Pierre 1943- Verfasser (DE-588)10785130X aut Microdifferential systems in the complex domain Pierre Schapira Berlin u.a. Springer 1985 X, 214 S. txt rdacontent n rdamedia nc rdacarrier Grundlehren der mathematischen Wissenschaften 269 Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Mikrolokale Analysis (DE-588)4169832-0 gnd rswk-swf Differentialoperator (DE-588)4012251-7 gnd rswk-swf Lineare partielle Differentialgleichung (DE-588)4167708-0 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Mikrolokale Analysis (DE-588)4169832-0 s Lineare partielle Differentialgleichung (DE-588)4167708-0 s Funktionentheorie (DE-588)4018935-1 s DE-604 Differentialgleichung (DE-588)4012249-9 s Algebraische Geometrie (DE-588)4001161-6 s Differentialoperator (DE-588)4012251-7 s Grundlehren der mathematischen Wissenschaften 269 (DE-604)BV000000395 269 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000152721&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Schapira, Pierre 1943- Microdifferential systems in the complex domain Grundlehren der mathematischen Wissenschaften Funktionentheorie (DE-588)4018935-1 gnd Mikrolokale Analysis (DE-588)4169832-0 gnd Differentialoperator (DE-588)4012251-7 gnd Lineare partielle Differentialgleichung (DE-588)4167708-0 gnd Algebraische Geometrie (DE-588)4001161-6 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| subject_GND | (DE-588)4018935-1 (DE-588)4169832-0 (DE-588)4012251-7 (DE-588)4167708-0 (DE-588)4001161-6 (DE-588)4012249-9 |
| title | Microdifferential systems in the complex domain |
| title_auth | Microdifferential systems in the complex domain |
| title_exact_search | Microdifferential systems in the complex domain |
| title_full | Microdifferential systems in the complex domain Pierre Schapira |
| title_fullStr | Microdifferential systems in the complex domain Pierre Schapira |
| title_full_unstemmed | Microdifferential systems in the complex domain Pierre Schapira |
| title_short | Microdifferential systems in the complex domain |
| title_sort | microdifferential systems in the complex domain |
| topic | Funktionentheorie (DE-588)4018935-1 gnd Mikrolokale Analysis (DE-588)4169832-0 gnd Differentialoperator (DE-588)4012251-7 gnd Lineare partielle Differentialgleichung (DE-588)4167708-0 gnd Algebraische Geometrie (DE-588)4001161-6 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| topic_facet | Funktionentheorie Mikrolokale Analysis Differentialoperator Lineare partielle Differentialgleichung Algebraische Geometrie Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000152721&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT schapirapierre microdifferentialsystemsinthecomplexdomain |