Positive convolution structure for a class of Heckman-Opdam hypergeometric functions of type BC |
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Authors: | Margit Rösler |
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Institution: | Institut für Mathematik, TU Clausthal, Erzstr. 1, D-38678 Clausthal-Zellerfeld, Germany |
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Abstract: | 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. |
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Keywords: | Hypergeometric functions associated with root systems Heckman-Opdam theory Hypergroups Grassmann manifolds |
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