Abstract
In this paper, we unify techniques of Pascal white noise analysis and harmonic analysis on configuration spaces establishing relations between the main structures of both ones. Fix a Random measure sigma on a Riemannian manifold X, we construct on the space of finite compound configuration space Omega(0) the so-called Lebesgue-Pascal measure lambda((sigma) over cap) and as a consequence we obtain the Pascal measure mu((sigma) over cap) on the compound configuration space Omega. Next, the natural realization of the symmetric Fock space over L-2(((sigma) over cap)) as the space L-2(lambda((sigma) over cap)) leads to the unitary isomorphism J(lambda mu) between the space L-2(lambda((sigma) over cap)) and L-2(mu((sigma) over cap)). Finally, in the first application we study some algebraic products, namely, the Borchers product on the Fock space, the Wick product on the Pascal space, and the star-convolution on the Lebesgue-Pascal space and we prove that the Pascal white noise analysis and harmonic analysis are related through an equality of operators involving J(lambda mu). The second application is devoted to solve the implementation problem.