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Algebraic Structures and Operator Calculus

Volume I: Representations and Probability Theory

  • Philip Feinsilver
  • René Schott

Part of the Mathematics and Its Applications book series (MAIA, volume 241)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Philip Feinsilver, René Schott
    Pages 1-8
  3. Philip Feinsilver, René Schott
    Pages 10-35
  4. Philip Feinsilver, René Schott
    Pages 36-41
  5. Philip Feinsilver, René Schott
    Pages 42-77
  6. Philip Feinsilver, René Schott
    Pages 78-126
  7. Philip Feinsilver, René Schott
    Pages 127-166
  8. Philip Feinsilver, René Schott
    Pages 167-195
  9. Philip Feinsilver, René Schott
    Pages 196-212
  10. Back Matter
    Pages 213-226

About this book

Introduction

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.

Keywords

Algebraic structure Bernoulli process Group representation Matrix Probability theory Representation theory algebra

Authors and affiliations

  • Philip Feinsilver
    • 1
  • René Schott
    • 2
  1. 1.Department of MathematicsSouthern Illinois UniversityCarbondaleUSA
  2. 2.CRINUniversité de Nancy IVandoeuvre-les-NancyFrance

Bibliographic information