Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Lie Theory 18 (2008), No. 3, 645--670Copyright Heldermann Verlag 2008 Asymptotic Harmonic Analysis on the Space of Square Complex Matrices Marouane Rabaoui Institut de Mathématiques de Jussieu, Université Pierre et Marie Curie, 175 rue de Chevaleret, 75013 Paris, France rabaoui@math.jussieu.fr [Abstract-pdf] This paper is largely of expository nature. We determine the spherical functions of positive type on the space $V_\infty= M(\infty, {\bf C})$ relatively to the action of the product group $K_\infty = U(\infty)\times U(\infty)$. The space $V_\infty$ is the inductive limit of the spaces of square complex matrices $V_n=M(n, {\bf C})$, and the group $K_\infty$ is the inductive limit of the product groups $K_n=U(n) \times U(n)$, where $U(n)$ is the unitary group. Keywords: Square complex matrices, unitary group, inductive limit, function of positive type, spherical function, ergodic measure, generalized Bochner theorem. MSC: 22E30; 43A35, 43A85, 43A90 [ Fulltext-pdf  (267  KB)] for subscribers only.