Symmetric Hilbert spaces and related topics infinitely divisible positive definite functions, continuous products and tensor products, Gaussian and Poissonian stochastic processes
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1972
|
| Schriftenreihe: | Lecture notes in mathematics
261 |
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| Online-Zugang: | Inhaltsverzeichnis |
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| 100 | 1 | |a Guichardet, Alain |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Symmetric Hilbert spaces and related topics |b infinitely divisible positive definite functions, continuous products and tensor products, Gaussian and Poissonian stochastic processes |c Alain Guichardet |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1972 | |
| 300 | |a V, 197 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 261 | |
| 650 | 4 | |a Hilbert, Espace de | |
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| 650 | 4 | |a Processus gaussiens | |
| 650 | 4 | |a Produits tensoriels | |
| 650 | 7 | |a Symmetrische ruimten |2 gtt | |
| 650 | 4 | |a Gaussian processes | |
| 650 | 4 | |a Hilbert space | |
| 650 | 4 | |a Positive-definite functions | |
| 650 | 4 | |a Tensor products | |
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| 650 | 0 | 7 | |a Funktionalanalysis |0 (DE-588)4018916-8 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102/MAT 001z 2001 B 999-261 |
|---|---|
| DE-BY-TUM_katkey | 487648 |
| DE-BY-TUM_media_number | 040020179684 |
| _version_ | 1816711536625844224 |
| adam_text | Table of Content
Introduction 1
Chapter 1. The symmetric measure space of a measure space. ... 3
1.1. The symmetric set of a set 3
1.2. The functor S on the category of sets 4
1.3. The symmetric Borel space of a Borel space ... 6
1.4. The symmetric measure space of a measure space . 7
1.5. Application to linear processes and factored
probability spaces 12
Chapter 2. The symmetric Hilbert space of a Hilbert space. ... 18
2.1. Definitions and general properties ....... 18
2.2. The unitary operators U. ^ and the groupS-u. . 22
A. f D f C q rl
2.3. Relation with symmetric measure spaces 28
Chapter 3. Positive definite functions of type (S) 30
3.1. Positive definite functions 30
3.2. Positive definite functions of type (S).
Definitions and first properties 35
3.3. The case of commutative locally compact groups . 38
Chapter 4. Conditionally positive definite functions and infi¬
nitely divisible positive definite functions 47
4.1. Conditionally positive definite matrices
and kernels 47
4.2. Conditionally positive definite functions on
groups 50
4.3. Infinitely divisible positive definite functions 56
Chapter 5. Boolean Algebras of tensor decompositions of a
Hilbert space 62
Chapter 6. Pactorizable positive definite functions on
current groups 80
6.1. Definitions 80
6.2. Results 82
6.3. Study of other current groups 90
Chapter 7. Gaussian measures on topological vector spaces. ... 93
7.1. Definitions and general properties 93
7.2. Relation with symmetric Hilbert spaces 96
7.3. Examples of Gaussian measures 100
7.4. The Wiener transform 103
7.5. Equivalence of Gaussian measures 105
IV
7.6. Quasi-invariance of Gaussian measures with
respect to translations 112
7.7. Ergodicity of Gaussian measures with respect
to rotations 115
Chapter 8. Continuous products 120
8.1. Introduction 120
8.2. Continuous products of complex numbers 121
8.3. Continuous tensor products of Hilbert spaces. . 126
8.4. Continuous tensor products of symmetric
Hilbert spaces 133
8.5. Continuous products of measure spaces 136
Appendix A. Infinite tensor products of Hilbert spaces 148
A.1. Definitions 148
A.2. Associativity and commutativity 149
A.3. Decomposable vectors 150
A.4. Tensor products of operators 153
Appendix B. Cohomology of groups 154
B.1. General definitions 154
B.2. Study of Z in the case of a unitary representation. . 154
Appendix C. Boolean algebras 157
C.1. General properties 157
C.2. tf -additive and d -multiplicative functions 160
C.3- Multiplicative measures 162
Appendix D. Restricted products of sets and measures 163
D.1. Restricted products of sets and Borel spaces 163
D.2. Measure spaces 165
D.3- Restricted products of measure spaces 166
Appendix E. Gaussian and Poissonian measures and processes. . . 168
E.1. Gaussian measures on Rn 168
E.2. Poissonian measures on R 169
E.3. Stochastic processes 169
Appendix F. Canonical commutation relations 172
Appendix G. Measures on topological vector spaces 174
G.1. General properties 174
G.2. Relation with linear stochastic processes 177
Appendix H. Conditional expectations and martingale theorem . . 179
H.1. Conditional expectations 179
H.2. The martingale theorem 180
H.3. Hellinger integrals and equivalence of measures. ... 180
Appendix I. Desintegration of continuous cocycles 182
V
Notation index 188
Terminological index 190
Bibliography 194
|
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| ctrlnum | (OCoLC)721195055 (DE-599)BVBBV003006855 |
| dewey-full | 510/.8 515/.73 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics 515 - Analysis |
| dewey-raw | 510/.8 515/.73 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV003006855 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-25T17:10:36Z |
| institution | BVB |
| isbn | 3540058036 9783540058038 0387058036 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001882369 |
| oclc_num | 721195055 |
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| physical | V, 197 S. |
| psigel | HUB-ZB011200907 |
| publishDate | 1972 |
| publishDateSearch | 1972 |
| publishDateSort | 1972 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spellingShingle | Guichardet, Alain Symmetric Hilbert spaces and related topics infinitely divisible positive definite functions, continuous products and tensor products, Gaussian and Poissonian stochastic processes Lecture notes in mathematics Hilbert, Espace de Hilbertruimten gtt Processus gaussiens Produits tensoriels Symmetrische ruimten gtt Gaussian processes Hilbert space Positive-definite functions Tensor products Hilbert-Raum (DE-588)4159850-7 gnd Funktionalanalysis (DE-588)4018916-8 gnd |
| subject_GND | (DE-588)4159850-7 (DE-588)4018916-8 |
| title | Symmetric Hilbert spaces and related topics infinitely divisible positive definite functions, continuous products and tensor products, Gaussian and Poissonian stochastic processes |
| title_auth | Symmetric Hilbert spaces and related topics infinitely divisible positive definite functions, continuous products and tensor products, Gaussian and Poissonian stochastic processes |
| title_exact_search | Symmetric Hilbert spaces and related topics infinitely divisible positive definite functions, continuous products and tensor products, Gaussian and Poissonian stochastic processes |
| title_full | Symmetric Hilbert spaces and related topics infinitely divisible positive definite functions, continuous products and tensor products, Gaussian and Poissonian stochastic processes Alain Guichardet |
| title_fullStr | Symmetric Hilbert spaces and related topics infinitely divisible positive definite functions, continuous products and tensor products, Gaussian and Poissonian stochastic processes Alain Guichardet |
| title_full_unstemmed | Symmetric Hilbert spaces and related topics infinitely divisible positive definite functions, continuous products and tensor products, Gaussian and Poissonian stochastic processes Alain Guichardet |
| title_short | Symmetric Hilbert spaces and related topics |
| title_sort | symmetric hilbert spaces and related topics infinitely divisible positive definite functions continuous products and tensor products gaussian and poissonian stochastic processes |
| title_sub | infinitely divisible positive definite functions, continuous products and tensor products, Gaussian and Poissonian stochastic processes |
| topic | Hilbert, Espace de Hilbertruimten gtt Processus gaussiens Produits tensoriels Symmetrische ruimten gtt Gaussian processes Hilbert space Positive-definite functions Tensor products Hilbert-Raum (DE-588)4159850-7 gnd Funktionalanalysis (DE-588)4018916-8 gnd |
| topic_facet | Hilbert, Espace de Hilbertruimten Processus gaussiens Produits tensoriels Symmetrische ruimten Gaussian processes Hilbert space Positive-definite functions Tensor products Hilbert-Raum Funktionalanalysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001882369&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT guichardetalain symmetrichilbertspacesandrelatedtopicsinfinitelydivisiblepositivedefinitefunctionscontinuousproductsandtensorproductsgaussianandpoissonianstochasticprocesses |