Hida distributions on compact Lie groups

We show that a nuclear space of analytic functions on K is associated with each compact, connected Lie group It. Its dual space consists of distributi ons (generalized functions on K) which correspond to the Hida distributions in white noise analysis. We extend Hall's transform to the space of Hida d istributions on K. This extension - the S-transform on K - is then used to characterize Hida. distributions by holomorphic: functions satisfying expon ential growth conditions IU-functions). We also give a tensor description o f Hida distributions which is induced by the Taylor may, on ti-functions. F inally we consider the Wiener path group over a complex, connected Lie grou p. We show that the Taylor map for square integrable holomorphic Wiener fun ctions is not isometric w.r.t. thf natural tensor norm. This indicates ((be sides other arguments) that there might be no generalization of Hida distri bution theory for (noncommutative) path groups equipped with Wiener measure .