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We consider a class of elliptic and parabolic differential operators with unbounded coefficients in R n , and we study the properties of the realization of such operators in suitable weighted L 2 spaces.

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Functions of bounded variation in an abstract Wiener space, i.e., an infinite-dimensional Banach space endowed with a Gaussian measure and a related differential structure, have been introduced by M. Fukushima and M. Hino using Dirichlet forms, and their properties have been studied with tools from analysis and stochastics. In this paper we reformulate, in an integral-geometric vein and with purely analytical tools, the definition and the main properties of BV functions, and investigate further properties.

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