Brownian motion and index formulas for the de Rham complex:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Berlin [u.a.]
Wiley-VCH
1998
|
| Edition: | 1. ed. |
| Series: | Mathematical research
106 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 215 S. graph. Darst. |
| ISBN: | 3527401393 |
Staff View
MARC
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| 245 | 1 | 0 | |a Brownian motion and index formulas for the de Rham complex |c Kazuaki Taira |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Wiley-VCH |c 1998 | |
| 300 | |a 215 S. |b graph. Darst. | ||
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| 650 | 0 | 7 | |a Kompakter Riemannscher Raum |0 (DE-588)4164858-4 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1804126804739358720 |
|---|---|
| adam_text | Table of Contents
Introduction 13
Chapter 1 Elements of Differential Geometry 33
1.1 Tangent Bundles 33
1.2 Vector Fields 35
1.3 Cotangent Bundles 39
1.4 Tensors 40
1.5 Tensors Fields 42
1.6 Exterior Product 43
1.7 Differential Forms 46
1.8 The de Rham Complex 48
1.9 The Codifferential, Hodge Star and Laplace Beltrami
Operators 49
Chapter 2 Elements of Functional Analysis 55
2.1 Transpose Operators 55
2.2 The Riesz Representation Theorem 56
2.3 Closed Operators 58
2.4 Compact Operators 59
2.5 The Riesz Schauder Theory 59
2.6 Fredholm Operators 61
2.7 Adjoint Operators 62
2.8 The Hilbert Schmidt Theory 64
2.9 Theory of Semigroups 65
Chapter 3 Elements of Markov Processes 69
3.1 Conditional Probabilities 69
3.2 Brownian Motion 70
12 Table of Contents
3.3 Markov Processes 71
3.4 Markov Transition Functions and Feller Semigroups 73
3.5 Theory of Feller Semigroups 78
Chapter 4 Elements of Partial Differential Equa¬
tions 85
4.1 Sobolev Spaces 85
4.2 Fourier Integral Operators 90
4.3 Pseudo Differential Operators 96
4.4 Pseudo Differential Operators on a Manifold 101
4.5 Elliptic Pseudo Differential Operators and their Indices 103
4.6 Potentials and Pseudo Differential Operators 115
4.7 Spaces of Currents 118
Chapter 5 Index Formulas for the de Rham Com¬
plex 121
5.1 The Boundaryless Case 121
5.2 The Bounded Case 127
Chapter 6 The Hodge—Kodaira Decomposition
Theorem 141
Chapter 7 The Exterior Derivative and the Co
differential Operator 147
7.1 Elementary Formulas 147
7.2 The Operators d and d* 152
7.3 The Relative Hodge Kodaira Decomposition Theorem 166
7.4 The Hodge Kodaira Decomposition Theorem with
Boundary Condition 173
Chapter 8 The Operator D 179
Chapter 9 The Long Exact Sequence and the Op¬
erator D 187
Chapter 10 Proof of Theorem 9.3 195
Bibliography 207
Subject Index 211
|
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| author | Taira, Kazuaki 1946- |
| author_GND | (DE-588)120483858 |
| author_facet | Taira, Kazuaki 1946- |
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| building | Verbundindex |
| bvnumber | BV012186828 |
| classification_rvk | SK 820 |
| ctrlnum | (OCoLC)845134131 (DE-599)BVBBV012186828 |
| discipline | Mathematik |
| edition | 1. ed. |
| format | Book |
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| id | DE-604.BV012186828 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:23:17Z |
| institution | BVB |
| isbn | 3527401393 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008259380 |
| oclc_num | 845134131 |
| open_access_boolean | |
| owner | DE-703 DE-824 DE-634 DE-11 |
| owner_facet | DE-703 DE-824 DE-634 DE-11 |
| physical | 215 S. graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Wiley-VCH |
| record_format | marc |
| series | Mathematical research |
| series2 | Mathematical research |
| spelling | Taira, Kazuaki 1946- Verfasser (DE-588)120483858 aut Brownian motion and index formulas for the de Rham complex Kazuaki Taira 1. ed. Berlin [u.a.] Wiley-VCH 1998 215 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematical research 106 Indexformel (DE-588)4617508-8 gnd rswk-swf Euler-Poincaré-Charakteristik (DE-588)4617768-1 gnd rswk-swf Kompakter Riemannscher Raum (DE-588)4164858-4 gnd rswk-swf DeRham-Komplex (DE-588)4617507-6 gnd rswk-swf Brownsche Bewegung (DE-588)4128328-4 gnd rswk-swf Brownsche Bewegung (DE-588)4128328-4 s DE-604 DeRham-Komplex (DE-588)4617507-6 s Indexformel (DE-588)4617508-8 s Kompakter Riemannscher Raum (DE-588)4164858-4 s Euler-Poincaré-Charakteristik (DE-588)4617768-1 s Mathematical research 106 (DE-604)BV000008585 106 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008259380&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Taira, Kazuaki 1946- Brownian motion and index formulas for the de Rham complex Mathematical research Indexformel (DE-588)4617508-8 gnd Euler-Poincaré-Charakteristik (DE-588)4617768-1 gnd Kompakter Riemannscher Raum (DE-588)4164858-4 gnd DeRham-Komplex (DE-588)4617507-6 gnd Brownsche Bewegung (DE-588)4128328-4 gnd |
| subject_GND | (DE-588)4617508-8 (DE-588)4617768-1 (DE-588)4164858-4 (DE-588)4617507-6 (DE-588)4128328-4 |
| title | Brownian motion and index formulas for the de Rham complex |
| title_auth | Brownian motion and index formulas for the de Rham complex |
| title_exact_search | Brownian motion and index formulas for the de Rham complex |
| title_full | Brownian motion and index formulas for the de Rham complex Kazuaki Taira |
| title_fullStr | Brownian motion and index formulas for the de Rham complex Kazuaki Taira |
| title_full_unstemmed | Brownian motion and index formulas for the de Rham complex Kazuaki Taira |
| title_short | Brownian motion and index formulas for the de Rham complex |
| title_sort | brownian motion and index formulas for the de rham complex |
| topic | Indexformel (DE-588)4617508-8 gnd Euler-Poincaré-Charakteristik (DE-588)4617768-1 gnd Kompakter Riemannscher Raum (DE-588)4164858-4 gnd DeRham-Komplex (DE-588)4617507-6 gnd Brownsche Bewegung (DE-588)4128328-4 gnd |
| topic_facet | Indexformel Euler-Poincaré-Charakteristik Kompakter Riemannscher Raum DeRham-Komplex Brownsche Bewegung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008259380&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000008585 |
| work_keys_str_mv | AT tairakazuaki brownianmotionandindexformulasforthederhamcomplex |