Stochastic processes and operator calculus on quantum groups:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht [u.a.]
Kluwer Academic Publishers
1999
|
| Schriftenreihe: | Mathematics and its applications
490 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VII, 227 S. |
| ISBN: | 079235883X |
Internformat
MARC
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| 100 | 1 | |a Franz, Uwe |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Stochastic processes and operator calculus on quantum groups |c by Uwe Franz and René Schott |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer Academic Publishers |c 1999 | |
| 300 | |a VII, 227 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematics and its applications |v 490 | |
| 650 | 4 | |a Calcul symbolique | |
| 650 | 7 | |a Calcul symbolique |2 ram | |
| 650 | 4 | |a Groupes quantiques | |
| 650 | 7 | |a Groupes quantiques |2 ram | |
| 650 | 7 | |a Kwantumgroepen |2 gtt | |
| 650 | 7 | |a Mathematische fysica |2 gtt | |
| 650 | 4 | |a Physique mathématique | |
| 650 | 7 | |a Physique mathématique |2 ram | |
| 650 | 4 | |a Processus stochastiques | |
| 650 | 7 | |a Processus stochastiques |2 ram | |
| 650 | 7 | |a Stochastische processen |2 gtt | |
| 650 | 4 | |a Mathematische Physik | |
| 650 | 4 | |a Quantum groups | |
| 650 | 4 | |a Stochastic processes | |
| 650 | 4 | |a Calculus, Operational | |
| 650 | 4 | |a Mathematical physics | |
| 650 | 0 | 7 | |a Quantengruppe |0 (DE-588)4252437-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Operatorenrechnung |0 (DE-588)4389717-4 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Schott, René |e Verfasser |4 aut | |
| 830 | 0 | |a Mathematics and its applications |v 490 |w (DE-604)BV008163334 |9 490 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009351492&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-009351492 | ||
Datensatz im Suchindex
| _version_ | 1804128498977079296 |
|---|---|
| adam_text | Contents
Preface vii
1 Introduction 1
2 Preliminaries on Lie groups 5
2.1 Basic definitions 5
2.2 Examples 7
2.3 Dual representations 9
2.4 The splitting lemma 15
2.5 The composition law 20
2.6 Matrix elements 22
2.7 Stochastic processes on Lie groups 24
3 Hopf algebras, quantum groups and braided spaces 45
3.1 Coalgebras, bialgebras, and Hopf algebras 46
3.2 Examples of bialgebras and Hopf algebras 50
3.3 Dual representations for quantum groups 58
3.4 A composition law for quantum groups 68
3.5 g Exponentials 73
3.6 Matrix elements 78
3.7 Braided tensor categories 81
3.8 Braided bialgebras and braided Hopf algebras 83
3.9 Examples of braided bialgebras and braided Hopf algebras 86
3.10 Braided spaces 88
3.11 Compact quantum groups 91
4 Stochastic processes on quantum groups 93
4.1 Quantum probability 93
4.2 Independence 94
4.3 Levy processes on bialgebras 96
4.4 Realisation of Levy processes on Fock spaces 98
4.5 Realisation of Levy processes by an inductive limit 102
4.6 Multiplicative stochastic integrals 105
4.7 Feynman Kac formula 106
4.8 Time reversal, duality, and R matrices 109
v
vi CONTENTS
5 Markov structure of quantum Levy processes 119
5.1 Classical versions of quantum Levy processes 120
5.2 Examples of classical versions of Levy processes on C,(a, a*) . . . 125
5.3 Examples of classical versions of Levy processes on Uq(si(2)) . . . 131
5.4 Levy processes on Uq(aff(l)) 136
6 Diffusions on braided spaces 139
6.1 A construction of (pseudo ) diffusions on braided spaces 140
6.2 Appell systems 146
6.3 Densities 150
7 Evolution equations and Levy processes on quantum groups 153
7.1 Appell systems 153
7.2 Wigner type densities 156
8 Gauss laws in the sense of Bernstein on quantum groups 161
8.1 Gaussian functionals in the sense of Bernstein 161
8.2 Uniqueness of embedding 171
8.3 Gaussian semi groups in the sense of Bernstein 175
9 Phase retrieval for probability distributions on quantum groups
and braided groups 183
9.1 Classical simply connected nilpotent Lie groups 184
9.2 The phase problem on the braided line 185
9.3 The phase problem on nilpotent quantum or braided groups .... 185
9.4 On the braided plane 187
9.5 On the braided Heisenberg Weyl group 187
10 Limit theorems on quantum groups 189
10.1 Analogues of the law of large numbers and the central limit theorem 189
10.2 A mixed quantum classical central limit theorem 191
10.3 Convergence to the Haar measure on compact quantum groups . . 198
10.4 ^ central limit theorem for Uq(su(2)) 198
10.5 Domains of attraction for g transformed random variables 206
Bibliography 215
Index 225
|
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| author | Franz, Uwe Schott, René |
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| dewey-search | 530.15/255 530.15/255 21 |
| dewey-sort | 3530.15 3255 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV013684976 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:50:12Z |
| institution | BVB |
| isbn | 079235883X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009351492 |
| oclc_num | 41712386 |
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| owner_facet | DE-703 DE-824 DE-521 |
| physical | VII, 227 S. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Kluwer Academic Publishers |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Franz, Uwe Verfasser aut Stochastic processes and operator calculus on quantum groups by Uwe Franz and René Schott Dordrecht [u.a.] Kluwer Academic Publishers 1999 VII, 227 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 490 Calcul symbolique Calcul symbolique ram Groupes quantiques Groupes quantiques ram Kwantumgroepen gtt Mathematische fysica gtt Physique mathématique Physique mathématique ram Processus stochastiques Processus stochastiques ram Stochastische processen gtt Mathematische Physik Quantum groups Stochastic processes Calculus, Operational Mathematical physics Quantengruppe (DE-588)4252437-4 gnd rswk-swf Operatorenrechnung (DE-588)4389717-4 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 s Operatorenrechnung (DE-588)4389717-4 s Quantengruppe (DE-588)4252437-4 s DE-604 Schott, René Verfasser aut Mathematics and its applications 490 (DE-604)BV008163334 490 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009351492&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Franz, Uwe Schott, René Stochastic processes and operator calculus on quantum groups Mathematics and its applications Calcul symbolique Calcul symbolique ram Groupes quantiques Groupes quantiques ram Kwantumgroepen gtt Mathematische fysica gtt Physique mathématique Physique mathématique ram Processus stochastiques Processus stochastiques ram Stochastische processen gtt Mathematische Physik Quantum groups Stochastic processes Calculus, Operational Mathematical physics Quantengruppe (DE-588)4252437-4 gnd Operatorenrechnung (DE-588)4389717-4 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4252437-4 (DE-588)4389717-4 (DE-588)4057630-9 |
| title | Stochastic processes and operator calculus on quantum groups |
| title_auth | Stochastic processes and operator calculus on quantum groups |
| title_exact_search | Stochastic processes and operator calculus on quantum groups |
| title_full | Stochastic processes and operator calculus on quantum groups by Uwe Franz and René Schott |
| title_fullStr | Stochastic processes and operator calculus on quantum groups by Uwe Franz and René Schott |
| title_full_unstemmed | Stochastic processes and operator calculus on quantum groups by Uwe Franz and René Schott |
| title_short | Stochastic processes and operator calculus on quantum groups |
| title_sort | stochastic processes and operator calculus on quantum groups |
| topic | Calcul symbolique Calcul symbolique ram Groupes quantiques Groupes quantiques ram Kwantumgroepen gtt Mathematische fysica gtt Physique mathématique Physique mathématique ram Processus stochastiques Processus stochastiques ram Stochastische processen gtt Mathematische Physik Quantum groups Stochastic processes Calculus, Operational Mathematical physics Quantengruppe (DE-588)4252437-4 gnd Operatorenrechnung (DE-588)4389717-4 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Calcul symbolique Groupes quantiques Kwantumgroepen Mathematische fysica Physique mathématique Processus stochastiques Stochastische processen Mathematische Physik Quantum groups Stochastic processes Calculus, Operational Mathematical physics Quantengruppe Operatorenrechnung Stochastischer Prozess |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009351492&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008163334 |
| work_keys_str_mv | AT franzuwe stochasticprocessesandoperatorcalculusonquantumgroups AT schottrene stochasticprocessesandoperatorcalculusonquantumgroups |