Abstract
Consider the Levy-Meixner one-mode interacting Fock space {Gamma(LM), <., .>(LM)}. Inspired by a derivative formula appearing in <., .>(LM), we define scalar products <., .>(LM,n) in symmetric n-particle spaces. Then, we introduce a class of one-mode type interacting Fock spaces Gamma(LM)(H) naturally associated to the one-dimensional infinitely divisible distributions with Levy-Meixner type {mu(r); r > 0}. The Fourier transform in generalized joint eigenvectors of a family {J(phi); phi is an element of epsilon} of Levy-Meixner Jacobi fields provides a way to explicit a unitary isomorphism U-LM between Gamma(LM)(H) and the so-called Levy-Meixner white noise space L-2(epsilon', B(epsilon'), Lambda(LM)). We derive a chaotic decomposition property of the quadratic integrable functionals of the Levy-Meixner white noise processes in terms of an appropriate Wick tensor product. For their stochastic regularity, we give explicit form and sharp estimate of the associated Donsker's delta function.