Nuclear Realization of Virasoro–Zamolodchikov-w∞ ⋆-Lie Algebras Through the Renormalized Higher Powers of Quantum Meixner White Noise

Abstract

By using an appropriate one-mode type interacting Fock spaces, [Formula: see text], introduced in [1], we define a nuclear triple [Formula: see text] of test and generalized functions, with θ 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 ⋆-Lie algebra and the Virasoro-Zamolodchikov-w∞ ⋆-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.