Abstract
By using an appropriate one-mode type interacting Fock spaces, Gamma(M)(H), introduced in [1], we define a nuclear triple F-M,F-theta(epsilon) subset of L-2(epsilon', Lambda(M)) subset of F-M,F-theta*(epsilon)of test and generalized functions, with theta being a suitable Young function. Moreover, we prove general characterization theorems for the fundamental nuclear spaces. For the applications, we introduce new renormalized products for the generators of the renormalized higher powers of white noise star-Lie algebra and the Virasoro-Zamolodchikov-omega(infinity) star-Lie algebra. Then we show that these new renormalized products lead to nuclear realizations of these Lie algebras in terms of quantum Meixner white noise operators.