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arXiv · 1902.09889

Characterization of BV functions on open domains: the Gaussian case and the general case

Davide Addona·Giorgio Menegatti·Michele Miranda Jr
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Abstract

We provide three different characterizations of the space $BV(O,\gamma)$ of the functions of bounded variation with respect to a centred non-degenerate Gaussian measure $ \gamma$ on open domains $O$ in Wiener spaces. Throughout these different characterizations we deduce a sufficient condition for belonging to $BV(O,\gamma)$ by means of the Ornstein-Uhlenbeck semigroup and we provide an explicit formula for one-dimensional sections of functions of bounded variation. Finally, we apply our technique to Fomin differentiable probability measures $\nu$ on a Hilbert space $X$, inferring a characterization of the space $BV(O,\nu)$ of the functions of bounded variation with respect to $\nu$ on open domains $O\subseteq X$.

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Davide Addona, Giorgio Menegatti, Michele Miranda Jr. 2019-02-26. Characterization of BV functions on open domains: the Gaussian case and the general case. https://arxiv.org/abs/1902.09889

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