Replacing the gaussian semigroup in the heat kernel estimates by the Ornstein-Uhlenbeck semigroup on , we define the notion of Kolmogorov kernel estimates. This allows us to show that under Dirichlet boundary conditions Ornstein-Uhlenbeck operators are generators of consistent, positive, (quasi-) contractive -semigroups on for all and for every domain . For exterior domains with sufficiently smooth boundary a result on the location of the spectrum of these operators is also given.
@article{ASNSP_2005_5_4_4_729_0, author = {Haller-Dintelmann, Robert and Wiedl, Julian}, title = {Kolmogorov kernel estimates for the {Ornstein-Uhlenbeck} operator}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {729--748}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 4}, number = {4}, year = {2005}, mrnumber = {2207741}, zbl = {1171.47302}, language = {en}, url = {http://www.numdam.org/item/ASNSP_2005_5_4_4_729_0/} }
TY - JOUR AU - Haller-Dintelmann, Robert AU - Wiedl, Julian TI - Kolmogorov kernel estimates for the Ornstein-Uhlenbeck operator JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2005 SP - 729 EP - 748 VL - 4 IS - 4 PB - Scuola Normale Superiore, Pisa UR - http://www.numdam.org/item/ASNSP_2005_5_4_4_729_0/ LA - en ID - ASNSP_2005_5_4_4_729_0 ER -
%0 Journal Article %A Haller-Dintelmann, Robert %A Wiedl, Julian %T Kolmogorov kernel estimates for the Ornstein-Uhlenbeck operator %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2005 %P 729-748 %V 4 %N 4 %I Scuola Normale Superiore, Pisa %U http://www.numdam.org/item/ASNSP_2005_5_4_4_729_0/ %G en %F ASNSP_2005_5_4_4_729_0
Haller-Dintelmann, Robert; Wiedl, Julian. Kolmogorov kernel estimates for the Ornstein-Uhlenbeck operator. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 4 (2005) no. 4, pp. 729-748. http://www.numdam.org/item/ASNSP_2005_5_4_4_729_0/
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