| Algebraic Structures and Operator Calculus: Volume I: Representations and Probability Theory 1993 Edition Contributor(s): Feinsilver, P. (Author), Schott, René (Author) |
|
 |
ISBN: 0792321162 ISBN-13: 9780792321163 Publisher: Springer OUR PRICE: $52.24 Product Type: Hardcover - Other Formats Published: January 1993 Annotation: This is the first of three volumes which present, in an original way, some of the most important tools of applied mathematics, in areas such as probability theory, operator calculus, representation theory, and special functions, used in solving problems in mathematics, physics and computer science. Volume I - Representations and Probability Theory - deals with probability theory in connection with group representations. It presents an introduction to Lie algebras and Lie groups which emphasises the connections with probability theory and representation theory. The book contains an introduction and seven chapters which treat, respectively, noncommutative algebra, hypergeometric functions, probability and Fock spaces, moment systems, Bernoulli processes/systems, and matrix elements. Each chapter contains exercises which range in difficulty from easy to advanced. The text is written so as to be suitable for self-study for both beginning graduate students and researchers. For students, teachers and researchers with an interest in algebraic structures and operator calculus. |
| Additional Information |
| BISAC Categories: - Mathematics | Mathematical Analysis - Computers | Computer Science - Mathematics | Algebra - Abstract |
| Dewey: 004 |
| LCCN: 92044824 |
| Series: Mathematics and Its Applications |
| Physical Information: 0.56" H x 6.14" W x 9.21" (1.13 lbs) 226 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |