Algebraic Structures and Operator Calculus : Volume I: Representations and Probability Theory / by Philip Feinsilver, René Schott
(Mathematics and Its Applications ; 241)
| データ種別 | 電子ブック |
|---|---|
| 出版者 | Dordrecht : Springer Netherlands : Imprint: Springer |
| 出版年 | 1993 |
| 本文言語 | 英語 |
| 大きさ | IX, 226 p : online resource |
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| 内容注記 | I. General remarks II. Some notations III. Gamma and beta functions IV. Numbering V. References VI. Polynomials: notations and formulas VII. Exercises and examples 1 Introductory Noncommutative Algebra I. Representations II. Heisenberg-Weyl algebra III. sl(2) algebra IV. Splitting formulas V. Exercises and examples 2 Hypergeometric functions I. Notations II. Generating function for 2F1 III. General formulation of CVPS and transformation formulas IV. Formulas related to HW algebra V. Formulas related to sl(2) algebra VI. Exercises and examples 3 Probability and Fock Spaces I. Trace functionals: probability and operators II. Fock spaces III. Tensor products IV. Exercises and examples 4 Moment Systems I. Moment generating functions and convolution II. Moment systems III. Radial moment systems IV. Holomorphic canonical variables V. Exercises and examples 5 Bernoulli Processes I. Bernoulli systems: general structure II. Binomial process and Krawtchouk polynomials III. Negative binomial process and Meixner polynomials IV. Continuous binomial process and Meixner-Pollaczek polynomials V. Poisson process and Poisson-Charlier polynomials VI. Exponential process and Laguerre polynomials VII. Brownian motion and Hermite polynomials VIII. Canonical moments IX. Exercises and examples 6 Bernoulli Systems I. Expansions, Rodrigues, and Riccati II. w-kernel III. X operator IV. Generating functions V. Riccati equations and Bernoulli systems VI. Reproducing kernels VII. Exercises 7 Matrix Elements I. Matrix elements II. Addition formulas and Riccati equations III. Coherent states and coherent state representations IV. Addition formulas for matrix elements of the group V. Exercises References |
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| 一般注記 | This series presents some tools of applied mathematics in the areas of proba bility theory, operator calculus, representation theory, and special functions used currently, and we expect more and more in the future, for solving problems in math ematics, physics, and, now, computer science. Much of the material is scattered throughout available literature, however, we have nowhere found in accessible form all of this material collected. The presentation of the material is original with the authors. The presentation of probability theory in connection with group represen tations is new, this appears in Volume I. Then the applications to computer science in Volume II are original as well. The approach found in Volume III, which deals in large part with infinite-dimensional representations of Lie algebras/Lie groups, is new as well, being inspired by the desire to find a recursive method for calcu lating group representations. One idea behind this is the possibility of symbolic computation of the matrix elements. In this volume, Representations and Probability Theory, we present an intro duction to Lie algebras and Lie groups emphasizing the connections with operator calculus, which we interpret through representations, principally, the action of the Lie algebras on spaces of polynomials. The main features are the connection with probability theory via moment systems and the connection with the classical ele mentary distributions via representation theory. The various systems of polynomi als that arise are one of the most interesting aspects of this study |
| 著者標目 | *Feinsilver, Philip author Schott, René author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Nonassociative rings LCSH:Rings (Algebra) LCSH:Topological groups LCSH:Lie groups LCSH:Operator theory LCSH:Special functions LCSH:Probabilities FREE:Mathematics FREE:Non-associative Rings and Algebras FREE:Topological Groups, Lie Groups FREE:Probability Theory and Stochastic Processes FREE:Special Functions FREE:Operator Theory |
| 分 類 | DC23:512.48 |
| 巻冊次 | ISBN:9789401116480 
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| ISBN | 9789401116480 |
| URL | http://dx.doi.org/10.1007/978-94-011-1648-0 |
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