0 Ju n 20 09 Riesz exponential families on homogeneous cones
نویسنده
چکیده
In this paper, we introduce, for a multiplier χ, a notion of generalized power function x 7→ ∆χ(x), defined on the homogeneous cone P of a Vinberg algebra A. We then extend to A the famous Gindikin result, that is we determine the set of multipliers χ such that the map θ 7→ ∆χ(θ), defined on P∗, is the Laplace transform of a positive measure Rχ. We also determine the set of χ such that Rχ generates an exponential family, and we calculate the variance function of this family.
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