CHARACTERIZATION THEOREMS IN GEGENBAUER WHITE NOISE THEORY

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 ′ β , a Gegenbauer white noise measure, Gβ , and construct a nuclear triple (Nβ) ⊂ L2(N ′ β ,Gβ) ⊂ (Nβ)∗ of test and generalized functions. A basic role is played by the chaos expansion. By using the Sβ -transform we prove a general characterization theorems for Gegenbauer white noise distributions, white noise test functions in terms of analytical functions.