Inserted: 12 jun 2009
Last Updated: 16 nov 2012
Journal: J. Funct. Anal.
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 integralgeometric vein and with purely analytical tools, the definition and the main properties of $BV$ functions, and investigate further properties.
Keywords: BV functions, Wiener spaces, Ornstein-Uhlenbeck semigroup