Geodesic
Some Fine Properties of BV Functions on Wiener Spaces
Analysis and Geometry in Metric Spaces, Tome 3 (2015) no. 1
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In this paper we define jump set and approximate limits for BV functions on Wiener spaces and show that the weak gradient admits a decomposition similar to the finite dimensional case. We also define the SBV class of functions of special bounded variation and give a characterisation of SBV via a chain rule and a closure theorem. We also provide a characterisation of BV functions in terms of the short-time behaviour of the Ornstein-Uhlenbeck semigroup following an approach due to Ledoux.
Mots-clés : Wiener space, functions of bounded variation 
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     author = {Ambrosio, Luigi and Miranda Jr., Michele and Pallara, Diego},
     title = {Some {Fine} {Properties} of {BV} {Functions} on {Wiener} {Spaces}},
     journal = {Analysis and Geometry in Metric Spaces},
     year = {2015},
     volume = {3},
     number = {1},
     zbl = {1321.26058},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AGMS_2015_3_1_a8/}
}
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Ambrosio, Luigi; Miranda Jr., Michele; Pallara, Diego. Some Fine Properties of BV Functions on Wiener Spaces. Analysis and Geometry in Metric Spaces, Tome 3 (2015) no. 1. http://geodesic.mathdoc.fr/item/AGMS_2015_3_1_a8/