ABSTRACT
There are four Laplacian operators in white noise distribution theory. We have already studied the Gross Laplacian Δ G and the number operator N in Chapter 10. We will study the semigroups associated with them in this chapter. The other two Laplacian operators are the Lévy Laplacian Δ L and the Volterra Laplacian Δ V . They are defined only for certain generalized functions and are often studied in terms of the S-transforms of these generalized functions.
