Journal of the
Korean Mathematical Society JKMS

Let the Gel'fand triple $ (E)_\beta \subset (L^2) \subset (E)_\beta^*$ be the framework of white noise distribution theory constructed by Kondratiev and Streit. A new class of continuous multiplicative products on $(E)_\beta$ is introduced and associated continuous derivations on $(E)_\beta$ are discussed. Algebraic characterizations of first order differential operators on $(E)_\beta$ are proved. Some applications are also discussed.

Keywords: white noise, derivation, first order differential operator, Cauchy problem, Poisson type equation

MSC numbers: 46F25