Displaying similar documents to “Analyticity of transition semigroups and closability of bilinear forms in Hilbert spaces”

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.

Kolmogorov kernel estimates for the Ornstein-Uhlenbeck operator

Robert Haller-Dintelmann, Julian Wiedl (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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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. ...

On analyticity of Ornstein-Uhlenbeck semigroups

Beniamin Goldys (1999)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Let ( R t be a transition semigroup of the Hilbert space-valued nonsymmetric Ornstein-Uhlenbeck process and let μ denote its Gaussian invariant measure. We show that the semigroup ( R t is analytic in L 2 ⁢ μ if and only if its generator is variational. In particular, we show that the transition semigroup of a finite dimensional Ornstein-Uhlenbeck process is analytic if and only if the Wiener process is nondegenerate.

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.

Analyticity for some degenerate one-dimensional evolution equations

G. Metafune (1998)

Studia Mathematica

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We study the analyticity of the semigroups generated by some degenerate second order differential operators in the space C([α,β]), where [α,β] is a bounded real interval. The asymptotic behaviour and regularity with respect to the space variable are also investigated.

On analytic semigroups and cosine functions in Banach spaces

V. Keyantuo, P. Vieten (1998)

Studia Mathematica

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If A generates a bounded cosine function on a Banach space X then the negative square root B of A generates a holomorphic semigroup, and this semigroup is the conjugate potential transform of the cosine function. This connection is studied in detail, and it is used for a characterization of cosine function generators in terms of growth conditions on the semigroup generated by B. The characterization relies on new results on the inversion of the vector-valued conjugate potential transform. ...