Time regularity for generalized Mehler semigroups

2020/12/23 by Lunardi, Alessandra
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2012.12797

Abstract

We study continuity and Hölder continuity of t↦ P_tf, where P_t is a generalized Mehler semigroup in C_b(X), the space of the continuous and bounded functions from a Banach space X to R, and f∈ C_b(X). The generators L of such semigroups are realizations of a class of differential and pseudo-differential operators, both in finite and in infinite dimension. Examples of operators L to which this theory is applicable include Ornstein-Uhlenbeck operators with fractional diffusion in finite dimension, and Ornstein-Uhlenbeck operators with associated strong-Feller semigroups, in infinite dimension.

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