WHITE NOISE ANALYSIS ON A NEW SPACE OF HIDA DISTRIBUTIONS

Let {α(n); n≥0} be a sequence of positive numbers satisfying certain conditions. A Gel'fand triple associated with the sequence {α (n); n ≥ 0} has been introduced on a white noise space (ℰ′,μ) by Cochran, Kuo and Sengupta. In this paper we obtain additional conditions on the sequence {α(n); n≥0} in order to carry out white noise distribution theory on the space (ℰ′,μ). Moreover, we show that the Bell numbers satisfy these additional conditions.