White noise calculus and Fock space:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin u.a.
Springer
1994
|
| Schriftenreihe: | Lecture notes in mathematics
1577 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 183 S. |
| ISBN: | 3540579850 0387579850 |
Internformat
MARC
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| 100 | 1 | |a Obata, Nobuaki |d 1957- |e Verfasser |0 (DE-588)113940424 |4 aut | |
| 245 | 1 | 0 | |a White noise calculus and Fock space |c Nobuaki Obata |
| 264 | 1 | |a Berlin u.a. |b Springer |c 1994 | |
| 300 | |a IX, 183 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1577 | |
| 650 | 7 | |a Functionaalintegratie |2 gtt | |
| 650 | 4 | |a Processus gaussiens | |
| 650 | 4 | |a Wiener, Intégrales de | |
| 650 | 4 | |a Gaussian processes | |
| 650 | 4 | |a Wiener integrals | |
| 650 | 0 | 7 | |a Fock-Raum |0 (DE-588)4223299-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Distribution |g Funktionalanalysis |0 (DE-588)4070505-5 |2 gnd |9 rswk-swf |
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| 830 | 0 | |a Lecture notes in mathematics |v 1577 |w (DE-604)BV000676446 |9 1577 | |
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Datensatz im Suchindex
| _version_ | 1805082775951245312 |
|---|---|
| adam_text |
Contents
Introduction vii
1 Prerequisites 1
1.1 Locally convex spaces in general 1
1.2 Countably Hilbert spaces 3
1.3 Nuclear spaces and kernel theorem 7
1.4 Standard CH spaces of functions 11
1.5 Bochner Minlos theorem 16
1.6 Further notational remarks 17
Bibliographical notes 18
2 White Noise Space 19
2.1 Gaussian measure 19
2.2 Wick ordered polynomials 23
2.3 Wiener Ito Segal isomorphism and Fock space 28
Bibliographical notes 32
3 White Noise Functional 33
3.1 Standard Construction 33
3.2 Continuous version theorem 38
3.3 S transform 48
3.4 Contraction of tensor products 53
3.5 Wiener product 58
3.6 Characterization theorems 65
Bibliographical notes 69
4 Operator Theory 71
4.1 Hida's differential operator 71
4.2 Translation operators 76
4.3 Integral kernel operators 79
4.4 Symbols of operators 88
4.5 Fock expansion 98
4.6 Some examples 100
Bibliographical notes 107
vi CONTENTS
5 Toward Harmonic Analysis 109
5.1 First order differential operators 109
5.2 Regular one parameter transformation group 118
5.3 Infinite dimensional Laplacians 121
5.4 Infinite dimensional rotation group 126
5.5 Rotation invariant operators 132
5.6 Fourier transform 140
5.7 Intertwining property of Fourier transform 145
Bibliographical notes 149
6 Addendum 151
6.1 Integral sum kernel operators 151
6.2 Reduction to finite degree of freedom 154
6.3 Vector valued white noise functionals 159
Appendices 167
A Polarization formula 167
B Hermite polynomials 168
C Norm estimates of contractions 169
References 171
Index 181 |
| any_adam_object | 1 |
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| dewey-raw | 510 515/.782 |
| dewey-search | 510 515/.782 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV009545611 |
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| indexdate | 2024-07-20T07:38:01Z |
| institution | BVB |
| isbn | 3540579850 0387579850 |
| language | English |
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| physical | IX, 183 S. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Obata, Nobuaki 1957- Verfasser (DE-588)113940424 aut White noise calculus and Fock space Nobuaki Obata Berlin u.a. Springer 1994 IX, 183 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1577 Functionaalintegratie gtt Processus gaussiens Wiener, Intégrales de Gaussian processes Wiener integrals Fock-Raum (DE-588)4223299-5 gnd rswk-swf Distribution Funktionalanalysis (DE-588)4070505-5 gnd rswk-swf Weißes Rauschen (DE-588)4189502-2 gnd rswk-swf Operator (DE-588)4130529-2 gnd rswk-swf Weißes Rauschen (DE-588)4189502-2 s Fock-Raum (DE-588)4223299-5 s DE-604 Operator (DE-588)4130529-2 s Distribution Funktionalanalysis (DE-588)4070505-5 s Lecture notes in mathematics 1577 (DE-604)BV000676446 1577 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006305663&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Obata, Nobuaki 1957- White noise calculus and Fock space Lecture notes in mathematics Functionaalintegratie gtt Processus gaussiens Wiener, Intégrales de Gaussian processes Wiener integrals Fock-Raum (DE-588)4223299-5 gnd Distribution Funktionalanalysis (DE-588)4070505-5 gnd Weißes Rauschen (DE-588)4189502-2 gnd Operator (DE-588)4130529-2 gnd |
| subject_GND | (DE-588)4223299-5 (DE-588)4070505-5 (DE-588)4189502-2 (DE-588)4130529-2 |
| title | White noise calculus and Fock space |
| title_auth | White noise calculus and Fock space |
| title_exact_search | White noise calculus and Fock space |
| title_full | White noise calculus and Fock space Nobuaki Obata |
| title_fullStr | White noise calculus and Fock space Nobuaki Obata |
| title_full_unstemmed | White noise calculus and Fock space Nobuaki Obata |
| title_short | White noise calculus and Fock space |
| title_sort | white noise calculus and fock space |
| topic | Functionaalintegratie gtt Processus gaussiens Wiener, Intégrales de Gaussian processes Wiener integrals Fock-Raum (DE-588)4223299-5 gnd Distribution Funktionalanalysis (DE-588)4070505-5 gnd Weißes Rauschen (DE-588)4189502-2 gnd Operator (DE-588)4130529-2 gnd |
| topic_facet | Functionaalintegratie Processus gaussiens Wiener, Intégrales de Gaussian processes Wiener integrals Fock-Raum Distribution Funktionalanalysis Weißes Rauschen Operator |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006305663&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT obatanobuaki whitenoisecalculusandfockspace |