Kolmogorov kernel estimates for the Ornstein-Uhlenbeck operator

Robert Haller-Dintelmann; Julian Wiedl

Displaying similar documents to “Kolmogorov kernel estimates for the Ornstein-Uhlenbeck operator”

Analyticity of transition semigroups and closability of bilinear forms in Hilbert spaces

Marco Fuhrman (1995)

Studia Mathematica

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We consider a semigroup acting on real-valued functions defined in a Hilbert space H, arising as a transition semigroup of a given stochastic process in H. We find sufficient conditions for analyticity of the semigroup in the $L^{2} (μ)$ space, where μ is a gaussian measure in H, intrinsically related to the process. We show that the infinitesimal generator of the semigroup is associated with a bilinear closed coercive form in $L^{2} (μ)$ . A closability criterion for such forms is presented. Examples are...

Estimates of the derivatives for a class of parabolic degenerate operators with unbounded coefficients in $ℝ^{N}$

Luca Lorenzi (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We consider a class of perturbations of the degenerate Ornstein-Uhlenbeck operator in $ℝ^{N}$ . Using a revised version of Bernstein’s method we provide several uniform estimates for the semigroup ${T (t)}_{t \geq 0}$ associated with the realization of the operator $𝒜$ in the space of all the bounded and continuous functions in $ℝ^{N}$

Injective semigroup-algebras

J. Green (1998)

Studia Mathematica

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Semigroups S for which the Banach algebra $ℓ^{1} (S)$ is injective are investigated and an application to the work of O. Yu. Aristov is described.

The domain of the Ornstein-Uhlenbeck operator on an $L^{p}$ -space with invariant measure

Giorgio Metafune, Jan Prüss, Abdelaziz Rhandi, Roland Schnaubelt (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We show that the domain of the Ornstein-Uhlenbeck operator on $L^{p}$ $(ℝ^{N}, μ d x)$ equals the weighted Sobolev space $W^{2, p} (ℝ^{N}, μ d x)$ , where $μ d x$ is the corresponding invariant measure. Our approach relies on the operator sum method, namely the commutative and the non commutative Dore-Venni theorems.

$L^{p}$ -spectrum of Ornstein-Uhlenbeck operators

Giorgio Metafune (2001)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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On the spectral bound of the generator of a $C_{0}$ -semigroup

Yu. Tomilov (1997)

Studia Mathematica

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We give several conditions implying that the spectral bound of the generator of a $C_{0}$ -semigroup is negative. Applications to stability theory are considered.

Functional calculi, regularized semigroups and integrated semigroups

Ralph deLaubenfels, Mustapha Jazar (1999)

Studia Mathematica

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We characterize closed linear operators A, on a Banach space, for which the corresponding abstract Cauchy problem has a unique polynomially bounded solution for all initial data in the domain of $A^{n}$ , for some nonnegative integer n, in terms of functional calculi, regularized semigroups, integrated semigroups and the growth of the resolvent in the right half-plane. We construct a semigroup analogue of a spectral distribution for such operators, and an extended functional calculus: When...

On a class of Markov type semigroups in spaces of uniformly continuous and bounded functions

Enrico Priola (1999)

Studia Mathematica

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We study a new class of Markov type semigroups (not strongly continuous in general) in the space of all real, uniformly continuous and bounded functions on a separable metric space E. Our results allow us to characterize the generators of Markov transition semigroups in infinite dimensions such as the heat and the Ornstein-Uhlenbeck semigroups.