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- W3011005522 abstract "Abstract We prove the equivalence of two different types of capacities in abstract Wiener spaces. This yields a criterion for the L p -uniqueness of the Ornstein-Uhlenbeck operator and its integer powers defined on suitable algebras of functions vanishing in a neighborhood of a given closed set Σ of zero Gaussian measure. To prove the equivalence we show the W r , p ( B , μ )-boundedness of certain smooth nonlinear truncation operators acting on potentials of nonnegative functions. We discuss connections to Gaussian Hausdorff measures. Roughly speaking, if L p -uniqueness holds then the ‘removed’ set Σ must have sufficiently large codimension, in the case of the Ornstein-Uhlenbeck operator for instance at least 2 p . For p = 2 we obtain parallel results on truncations, capacities and essential self-adjointness for Ornstein-Uhlenbeck operators with linear drift. These results apply to the time zero Gaussian free field as a prototype example." @default.
- W3011005522 created "2020-03-23" @default.
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- W3011005522 date "2020-03-14" @default.
- W3011005522 modified "2023-10-05" @default.
- W3011005522 title "Capacities, Removable Sets and Lp-Uniqueness on Wiener Spaces" @default.
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- W3011005522 doi "https://doi.org/10.1007/s11118-020-09836-6" @default.
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