Asymptotic Harmonic Analysis on the Space of Square Complex Matrices

M. Rabaoui

Journal of Lie theory, Tome 18 (2008) no. 3, pp. 645-67.

Résumé

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.

Détail

Classification : 22E30, 43A35, 43A85, 43A90
Mots-clés : Square complex matrices, unitary group, inductive limit, function of positive type, spherical function, ergodic measure, generalized Bochner theorem