Harmonic Analysis and Special Functions on Symmetric Spaces

Harmonic Analysis and Special Functions on Symmetric Spaces

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This text is derived from lecture notes for the European School of Group Theory, a forum providing high-level courses on recent developments in group theory. The topic is elaborated with statements of definitions and theorems; these in turn are augmented with examples. The authors extend the ideas of harmonic analysis on semisimple symmetric spaces to embrace the theory of hypergeometric and spherical functions to show that the K-variant Eisenstein integrals for G/H are hypergeometric functions under this theory. They lead readers from the fundamentals of semisimple symmetric spaces of G/H to the frontier, including generalization, to the Reimannian case.
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Product details

  • Hardback | 256 pages
  • 157.48 x 233.68 x 20.32mm | 589.67g
  • Academic Press Inc
  • San Diego, United States
  • English
  • index
  • 0123361702
  • 9780123361707

Table of contents

Part 1 The hypergeometric differential operators: the periodic Calogero-Moser system; the hypergeometric shift operators; the hypergeometric function; spherical functions of type x. Part 2 Structure theory: parabolic subgroups; invariant differential operators; principal series representations; spherical distributions; the Fourier transform; wave packets. Part 3 The generalized Cartan decomposition (after B. Hoogenboom); the spectral problems for hypergeometric functions associated with a root system; the case of the Gaussian hypergeometric function; open problems.
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