Ornstein-Uhlenbeck Semigroup on the dual space of Gelfand-Shilov Spaces of Beurling type

Abstract

We use a previously obtained topological characterization of Gelfand-Shilov spaces of Beurling type to characterize its dual using Riesz representation theorem. Using the characterization of the dual space equipped with the weak topology, we study the action of Ornstein-Uhlenbeck Semigroup on the dual space.