We provide three different characterizations of the space BV (O, γ) of the functions of bounded variation with respect to a centred non-degenerate Gaussian measure γ on open domains O in Wiener spaces. Throughout these different characterizations we deduce a sufficient condition in order to belong to BV (O, γ) 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 techniques to Fomin differentiable probability measures ν on a Hilbert space X, and we infer a characterization of the space BV (O, ν) of the functions of bounded variation with respect to ν on open domains O ⊆ X.

BV functions on open domains: The wiener case and a fomin differentiable case / Addona, D.; Menegatti, G.; Miranda, M.. - In: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS. - ISSN 1534-0392. - 19:5(2020), pp. 2679-2711. [10.3934/CPAA.2020117]

BV functions on open domains: The wiener case and a fomin differentiable case

Addona D.
;
Menegatti G.;Miranda M.
2020

Abstract

We provide three different characterizations of the space BV (O, γ) of the functions of bounded variation with respect to a centred non-degenerate Gaussian measure γ on open domains O in Wiener spaces. Throughout these different characterizations we deduce a sufficient condition in order to belong to BV (O, γ) 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 techniques to Fomin differentiable probability measures ν on a Hilbert space X, and we infer a characterization of the space BV (O, ν) of the functions of bounded variation with respect to ν on open domains O ⊆ X.
BV functions on open domains: The wiener case and a fomin differentiable case / Addona, D.; Menegatti, G.; Miranda, M.. - In: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS. - ISSN 1534-0392. - 19:5(2020), pp. 2679-2711. [10.3934/CPAA.2020117]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/2907264
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