arXiv subjects
Publications and source records attributed to D. Pallara.
We consider generalised Mehler semigroups and, assuming the existence of an associated invariant measure $σ$, we prove functional integral inequalities with respect to $σ$, such as logarithmic Sobolev and Poincaré type. Consequently, some integrability properties of exponential functions with respect to $σ$ are deduced.
We study functions of bounded variation (and sets of finite perimeter) on a convex open set $Ω\subseteq X$, $X$ being an infinite dimensional real Hilbert space. We relate the total variation of such functions, defined through an integration by parts formula, to the short-time behaviour of the semigroup associated with a perturbation of the Ornstein--Uhlenbeck operator.
We present the foundations of the theory of functions of bounded variation and sets of finite perimeter in abstract Wiener spaces.