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On functions of bounded variation on convex domains in Hilbert spaces
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On functions of bounded variation on convex domains in Hilbert spaces
classification
math.FA
math.AP
keywords
functionsvariationboundedconvexhilbertassociatedbehaviourdefined
abstract
We study functions of bounded variation (and sets of finite perimeter) on a convex open set $\Omega\subseteq X$, $X$ 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.
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