On the Laplacian on a space of white noise functionals (Q1904462)

This paper studies the Laplacian operator on a space of white noise functionals, with applications to mathematical physics in mind. One of the main features is that the usual weak derivative is replaced by the Hida differential. This allows to generalize in some sense the general theory of Arai-Mitoma. The operator associated to the Hida differential is then defined and used to build the Laplacian according with de Rham theory. This operator has some nice invariant properties. De Rham complexes and de Rham-Hodge-Kodaira decompositions are studied in detail. Functional analysis, and in particular spectral theory, play an important role in the constructions. Explicit expressions for the Laplacian are also considered with some extension.