by Debabrata Basu (Indian Institute of Technology, India)

Table of Contents (96k)
Foreword (54k)
Preface (64k)

This book is suitable for use in any graduate course on analytical methods and their application to representation theory. Each concept is developed with special emphasis on lucidity and clarity. The book also shows the direct link of Cauchy–Pochhammer theory with the Hadamard–Reisz–Schwartz–Gel'fand et al. regularization. The flaw in earlier works on the Plancheral formula for the universal covering group of SL(2,R) is pointed out and rectified. This topic appears here for the first time in the correct form.

Existing treatises are essentially magnum opus of the experts, intended for other experts in the field. This book, on the other hand, is unique insofar as every chapter deals with topics in a way that differs remarkably from traditional treatment. For example, Chapter 3 presents the Cauchy–Pochhammer theory of gamma, beta and zeta function in a form which has not been presented so far in any treatise of classical analysis.

• Analysis:
  • Basic Analytical Tools
  • Complex Integration
  • The Gamma, Beta and Zeta Function of Riemann
  • The Special Functions Defined by Power Series
  • Bargman–Segal Spaces of Analytic Functions
  • Elements of the Theory of Generalized Functions
• Applications to Group Representation Theory:
  • Lie Groups and Their Representations
  • The Three-Dimensional Rotation Group and SU(2) and Elements of SU(3)
  • The Three-Dimensional Lorentz Group
  • The Four-Dimensional Lorentz Group
  • The Heisenberg–Weyl Group and the Bargmann–Segal Spaces