TY  - JOUR
AB  - We prove the equivalence of two different types of capacities in abstract Wiener spaces. This yields a criterion for theL(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 sigma of zero Gaussian measure. To prove the equivalence we show theW(r,p)(B,mu)-boundedness of certain smooth nonlinear truncation operators acting on potentials of nonnegative functions. We discuss connections to Gaussian Hausdorff measures. Roughly speaking, ifL(p)-uniqueness holds then the 'removed' set sigma must have sufficiently large codimension, in the case of the Ornstein-Uhlenbeck operator for instance at least 2p. Forp= 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.
DA  - 2021
DO  - 10.1007/s11118-020-09836-6
KW  - Wiener spaces
KW  - Capacities
KW  - Ornstein-Uhlenbeck operator
KW  - Sobolev spaces
KW  - Composition operators
KW  - L-p-uniqueness
LA  - eng
M2  - 503–533
PY  - 2021
SN  - 0926-2601
SP  - 503–533-
T2  - Potential Analysis
TI  - Capacities, Removable Sets andL(p)-Uniqueness on Wiener Spaces
UR  - https://nbn-resolving.org/urn:nbn:de:0070-pub-29458438
Y2  - 2024-11-21T20:59:55
ER  -