Displaying similar documents to “The domain of the Ornstein-Uhlenbeck operator on an L p -space with invariant measure”

Kolmogorov kernel estimates for the Ornstein-Uhlenbeck operator

Robert Haller-Dintelmann, Julian Wiedl (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Similarity:

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. ...

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

Marco Fuhrman (1995)

Studia Mathematica

Similarity:

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...

A central limit theorem on the space of positive definite symmetric matrices

Piotr Graczyk (1992)

Annales de l'institut Fourier

Similarity:

A central limit theorem is proved on the space 𝒫 n of positive definite symmetric matrices. To do this, some natural analogs of the mean and dispersion on 𝒫 n are defined and investigated. One uses a Taylor expansion of the spherical functions on 𝒫 n .

A C * -algebraic Schoenberg theorem

Ola Bratteli, Palle E. T. Jorgensen, Akitaka Kishimoto, Donald W. Robinson (1984)

Annales de l'institut Fourier

Similarity:

Let 𝔄 be a C * -algebra, G a compact abelian group, τ an action of G by * -automorphisms of 𝔄 , 𝔄 τ the fixed point algebra of τ and 𝔄 F the dense sub-algebra of G -finite elements in 𝔄 . Further let H be a linear operator from 𝔄 F into 𝔄 which commutes with τ and vanishes on 𝔄 τ . We prove that H is a complete dissipation if and only if H is closable and its closure generates a C 0 -semigroup of completely positive contractions. These complete dissipations are classified in terms of certain twisted negative...

Perturbation of analytic operators and temporal regularity of discrete heat kernels

Sönke Blunck (2000)

Colloquium Mathematicae

Similarity:

In analogy to the analyticity condition ∥ A e t A ∥ ≤ C t - 1 , t > 0, for a continuous time semigroup ( e t A ) t ≥ 0 , a bounded operator T is called analytic if the discrete time semigroup ( T n ) n ∈ ℕ satisfies ∥ ( T - I ) T n ∥ ≤ C n - 1 , n ∈ ℕ. We generalize O. Nevanlinna’s characterization of powerbounded and analytic operators T to the following perturbation result: if S is a perturbation of T such that ∥ R ( λ 0 , T ) - R ( λ 0 , S ) ∥ is small enough for some λ 0 ∈ ϱ ( T ) ∩ ϱ ( S ) , then the type ω of the semigroup ( e t ( S - I ) ) also controls the analyticity of S in the sense that ∥ ( S - I ) S n ∥ ≤ C ( ω + n - 1 ) e ω n , n ∈ ℕ. As an application...

Is A - 1 an infinitesimal generator?

Hans Zwart (2007)

Banach Center Publications

Similarity:

In this paper we study the question whether A - 1 is the infinitesimal generator of a bounded C₀-semigroup if A generates a bounded C₀-semigroup. If the semigroup generated by A is analytic and sectorially bounded, then the same holds for the semigroup generated by A - 1 . However, we construct a contraction semigroup with growth bound minus infinity for which A - 1 does not generate a bounded semigroup. Using this example we construct an infinitesimal generator of a bounded semigroup for which its...