Holomorphicity of a class of semigroups of measures operating on 𝐿^{𝑝}(𝐺/𝐻)

Abstract

In the present paper we consider the class of stable semigroups of measures on a Lie group G G . This class contains the Gaussian semigroups. We prove that under certain strongly continuous representations of G G acting in L p ( G / H ) {L^p}(G/H) , 1 ⩽ p > ∞ 1 \leqslant p > \infty , these semigroups are holomorphic and uniformly bounded.