Analytic aspects of Poissonian white noise analysis

Abstract

General structures of Poissonian white noise analysis are presented.Simultaneously, the theory is developed on Poisson and Lebesgue- Poisson space. Both spaces have an own S-transform, well known in the Gaussian case. They give an extra connection between these two spaces via the Bargmann-Segal space. Test and generalized functions,different types of convolutions, and representations of creation and annihilation operators in the aforementioned spaces are considered.