Diffuse and discrete semigroups of probability measures on Abelian Hilbert-Lie groups

Abstract

In the present paper we investigate diffuse and discrete measures on abelian Hilbert-Lie groups and give the answer to the question that each Gaussian con-volution semigroup is diffuse.

Keywords

• continuous convolution semigroup
• gaussian convolution semigroup
• operator semigroup
• discrete measure
• diffuse measure
• hilbert-lie group
• l´evy measure
• infinitesimal generator of local character
• generating functional
• semi-bounded functional