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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 ${(G (n), K (n))}_{n \geq 1}$ . 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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