On the Theta semigroup
  In this paper we consider a semigroup on trigonometric expansions that will be called the Theta semigroup since its kernel is a multiple of the third Jacobi theta function. We study properties of this semigroup and prove that it is a positive diffusion semigroup. We also obtain that its subordinated semigroup is the classical Poisson semigroup. The extensions to higher dimensions and to periodic ultra distributions are also considered. 
Ahmed Zayed and Wilfredo Urbina
math.CA