Kolmogorov kernel estimates for the Ornstein-Uhlenbeck operator
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 4 (2005) no. 4, p. 729-748

Replacing the gaussian semigroup in the heat kernel estimates by the Ornstein-Uhlenbeck semigroup on ${ℝ}^{d}$, 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 ${C}_{0}$-semigroups on ${L}^{p}\left(\Omega \right)$ for all $1\le p<\infty$ and for every domain $\Omega \subseteq {ℝ}^{d}$. For exterior domains with sufficiently smooth boundary a result on the location of the spectrum of these operators is also given.

Classification:  47D06,  35K20
@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},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 4},
number = {4},
year = {2005},
pages = {729-748},
zbl = {1171.47302},
mrnumber = {2207741},
language = {en},
url = {http://www.numdam.org/item/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, Serie 5, Volume 4 (2005) no. 4, pp. 729-748. http://www.numdam.org/item/ASNSP_2005_5_4_4_729_0/

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