Hypergeometric functions associated to cones of convex type in a Euclidean Jordan algebra

摘要

In this paper, we study a family of hypergeometric functions associated to cones of convex type in a Euclidean Jordan algebra. We obtain upper and lower bounds and give information about their singularities. The family under consideration was introduced by Sahi (Invent. Math. 110 (1992), 409-418) and it plays an important role in the construction of some small representations. (C) 2002 Elsevier Seienee (USA). [References: 7]