Abstract
The main purpose of this paper is to derive a general structure of Gegenbauer white noise analysis as a counterpart class of non-Levy white noise. Namely, we consider, on an appropriate space of distributions, N-beta(1), a Gegenbauer white noise measure, G(beta), and construct a nuclear triple (N-beta) subset of L-2 (N-beta(1), G(beta)) subset of (N-beta)* of test and generalized functions. A basic role is played by the chaos expansion. By using the S-beta-transform we prove a general characterization theorems for Gegenbauer white noise distributions, white noise test functions in terms of analytical functions.