Uniformly Bounded Representations of the Universal Covering Group of Sl(2,ü?)

In a recent paper, Pukanszky [6] has classified all the irreducible unitary representations of the universal covering group G of Gi = SL(2, R). We construct analytic continuations of the "principal series" of representations of G into certain domains in the complex plane. The representations obtained by continuation are uniformly bounded and, in special cases, they are equivalent to those constructed for Gi by Kunze and Stein in [4]. In the course of the investigation, several interesting connections with special functions occur. Full details and proofs will be published elsewhere.