Positive convolution structure for a class of Heckman–Opdam hypergeometric functions of type BC
نویسندگان
چکیده
منابع مشابه
Positive convolution structure for a class of Heckman-Opdam hypergeometric functions of type BC
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 thes...
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Let FBC(λ, k; t) be the Heckman-Opdam hypergeometric function of type BC with multiplicities k = (k1, k2, k3) and weighted half sum ρ(k) of positive roots. We prove that FBC(λ + ρ(k), k; t) converges for k1 + k2 → ∞ and k1/k2 → ∞ to a function of type A for t ∈ R and λ ∈ C. This limit is obtained from a corresponding result for Jacobi polynomials of type BC, which is proven for a slightly more ...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2010
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2009.12.007