Kolmogorov kernel estimates for the Ornstein-Uhlenbeck operator

Robert Haller-Dintelmann[1]; Julian Wiedl[1]

  • [1] Technische Universität Darmstadt Fachbereich Mathematik Schlossgartenstr. 7 D-64289 Darmstadt, Germany

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2005)

  • Volume: 4, Issue: 4, page 729-748
  • ISSN: 0391-173X

Abstract

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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 ( Ω ) for all 1 ≤ p < ∞ and for every domain Ω ⊆ ℝ d . For exterior domains with sufficiently smooth boundary a result on the location of the spectrum of these operators is also given.

How to cite

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Haller-Dintelmann, Robert, and Wiedl, Julian. "Kolmogorov kernel estimates for the Ornstein-Uhlenbeck operator." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 4.4 (2005): 729-748. <http://eudml.org/doc/84578>.

@article{Haller2005,
abstract = {Replacing the gaussian semigroup in the heat kernel estimates by the Ornstein-Uhlenbeck semigroup on $\mathbb \{R\}^d$, 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 $L^p(\Omega )$ for all $1 \le p &lt; \infty $ and for every domain $\Omega \subseteq \mathbb \{R\}^d$. For exterior domains with sufficiently smooth boundary a result on the location of the spectrum of these operators is also given.},
affiliation = {Technische Universität Darmstadt Fachbereich Mathematik Schlossgartenstr. 7 D-64289 Darmstadt, Germany; Technische Universität Darmstadt Fachbereich Mathematik Schlossgartenstr. 7 D-64289 Darmstadt, Germany},
author = {Haller-Dintelmann, Robert, Wiedl, Julian},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {4},
pages = {729-748},
publisher = {Scuola Normale Superiore, Pisa},
title = {Kolmogorov kernel estimates for the Ornstein-Uhlenbeck operator},
url = {http://eudml.org/doc/84578},
volume = {4},
year = {2005},
}

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
PB - Scuola Normale Superiore, Pisa
VL - 4
IS - 4
SP - 729
EP - 748
AB - Replacing the gaussian semigroup in the heat kernel estimates by the Ornstein-Uhlenbeck semigroup on $\mathbb {R}^d$, 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 $L^p(\Omega )$ for all $1 \le p &lt; \infty $ and for every domain $\Omega \subseteq \mathbb {R}^d$. For exterior domains with sufficiently smooth boundary a result on the location of the spectrum of these operators is also given.
LA - eng
UR - http://eudml.org/doc/84578
ER -

References

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