Journal
JOURNAL OF FUNCTIONAL ANALYSIS
Volume 258, Issue 8, Pages 2779-2800Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jfa.2009.12.007
Keywords
Hypergeometric functions associated with root systems; Heckman-Opdam theory; Hypergroups; Grassmann manifolds
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In this paper, we derive explicit product formulas and positive convolution structures for three continuous classes of Heckman-Opdam hypergeometric functions of type BC. For specific discrete series of multiplicities these hypergeometric functions occur as the spherical functions of non-compact Grassmann manifolds G/K over one of the skew fields F = R, C, H. We write the product formula of these spherical functions in an explicit form which allows analytic continuation with respect to the parameters. In each of the three cases, we obtain a series of hypergroup algebras which include the commutative convolution algebras of K-biinvariant functions on G as special cases. The characters are given by the associated hypergeometric functions. (C) 2009 Elsevier Inc. All rights reserved.
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