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A Bochner type theorem for inductive limits of Gelfand pairs

Marouane Rabaoui — 2008

Annales de l’institut Fourier

In this article, we prove a generalisation of Bochner-Godement theorem. Our result deals with Olshanski spherical pairs ( G , K ) defined as inductive limits of increasing sequences of Gelfand pairs ( G ( n ) , K ( n ) ) n 1 . By using the integral representation theory of G. Choquet on convex cones, we establish a Bochner type representation of any element ϕ of the set 𝒫 ( G ) of K -biinvariant continuous functions of positive type on G .

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