An analytic family of uniformly bounded representations of free groups

Abstract

Harmonic analysis on a free group F has attracted considerable attention in the last ten years or so. There seem to be two reason for that: one is the discovery of deep analogy of certain aspects of harmonic analysis on a free group and harmonic analysis on SL(2,R), cf. e.g. fundamental works of P. Cartier [4], A. Figa-Talamanca and M. A. Picardello [8], the other being the interest in the C∗-algebra generated by the regular representation of F , cf. A. Connes [5], J. Cuntz [6], U. Haagerup [10], M. Pimsner and D. Voiculescu [14].