Algebraic structures and operator calculus: 1 Representations and probability theory
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht u.a.
Kluwer
1993
|
| Series: | Mathematics and its applications
241 |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 223 S. |
| ISBN: | 0792321162 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Table of Contents
Preface ix
Introduction
I. General remarks 1
II. Some notations 2
III. Gamma and beta functions 3
IV. Numbering 5
V. References 5
VI. Polynomials: notations and formulas 5
VII. Exercises and examples 8
Chapter 1 Introductory Noncommutative Algebra
I. Representations 9
II. Heisenberg Weyl algebra 12
III. sl(2) algebra 18
IV. Splitting formulas 24
V. Exercises and examples 28
Chapter 2 Hypergeometric functions
I. Notations 35
II. Generating function for 2^1 35
III. General formulation of CVPS and transformation formulas 36
IV. Formulas related to HW algebra 37
V. Formulas related to sl(2) algebra 38
VI. Exercises and examples 39
Chapter 3 Probability and Fock Spaces
I. Trace functionals: probability and operators 41
II. Fock spaces 48
III. Tensor products 62
IV. Exercises and examples 72
Chapter 4 Moment Systems
I. Moment generating functions and convolution 77
II. Moment systems 83
III. Radial moment systems 92
IV. Holomorphic canonical variables 104
V. Exercises and examples 113
vii
Chapter 5 Bernoulli Processes
I. Bernoulli systems: general structure 126
II. Binomial process and Krawtchouk polynomials 136
III. Negative binomial process and Meixner polynomials 140
IV. Continuous binomial process and Meixner Pollaczek polynomials 142
V. Poisson process and Poisson Charlier polynomials 145
VI. Exponential process and Laguerre polynomials 151
VII. Brownian motion and Hermite polynomials 155
VIII. Canonical moments 160
IX. Exercises and examples 162
Chapter 6 Bernoulli Systems
I. Expansions, Rodrigues, and Riccati 166
II. w kernel 172
III. X operator 173
IV. Generating functions 177
V. Riccati equations and Bernoulli systems 180
VI. Reproducing kernels 186
VII. Exercises 193
Chapter 7 Matrix Elements
I. Matrix elements 195
II. Addition formulas and Riccati equations 199
III. Coherent states and coherent state representations 201
IV. Addition formulas for matrix elements of the group 207
V. Exercises 211
References 213
Index 217
viii
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| id | DE-604.BV006620484 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:49:23Z |
| institution | BVB |
| isbn | 0792321162 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-004230984 |
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| physical | IX, 223 S. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Kluwer |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Feinsilver, Philip J. Verfasser aut Algebraic structures and operator calculus 1 Representations and probability theory by Philip Feinsilver and René Schott Dordrecht u.a. Kluwer 1993 IX, 223 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 241 Mathematics and its applications ... Schott, René Verfasser aut (DE-604)BV006620483 1 Mathematics and its applications 241 (DE-604)BV008163334 241 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004230984&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Feinsilver, Philip J. Schott, René Algebraic structures and operator calculus Mathematics and its applications |
| title | Algebraic structures and operator calculus |
| title_auth | Algebraic structures and operator calculus |
| title_exact_search | Algebraic structures and operator calculus |
| title_full | Algebraic structures and operator calculus 1 Representations and probability theory by Philip Feinsilver and René Schott |
| title_fullStr | Algebraic structures and operator calculus 1 Representations and probability theory by Philip Feinsilver and René Schott |
| title_full_unstemmed | Algebraic structures and operator calculus 1 Representations and probability theory by Philip Feinsilver and René Schott |
| title_short | Algebraic structures and operator calculus |
| title_sort | algebraic structures and operator calculus representations and probability theory |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004230984&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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