Analyticity for some degenerate one-dimensional evolution equations

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On the growth of analytic semigroups along vertical lines

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We construct two Banach algebras, one which contains analytic semigroups ${(a^{z})}_{R e z > 0}$ such that $| a^{1 + i y} | \to \infty$ arbitrarily slowly as $| y | \to \infty$ , the other which contains ones such that $| a^{1 + i y} | \to \infty$ arbitrarily fast

Notes on Analytic Convoluted $C$ -semigroups

Marko Kostić (2010)

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Analyticity of absorption semigroups.

M. Ishikawa (1995)

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

Marco Fuhrman (1995)

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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...

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

Enrico Priola (1999)

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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.

On α-times integrated C-semigroups and the abstract Cauchy problem

Chung-Cheng Kuo, Sen-Yen Shaw (2000)

Studia Mathematica

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This paper is concerned with α-times integrated C-semigroups for α > 0 and the associated abstract Cauchy problem: $u^{'} (t) = A u (t) + \frac{t^{α - 1}}{Γ (α)} x$ , t >0; u(0) = 0. We first investigate basic properties of an α-times integrated C-semigroup which may not be exponentially bounded. We then characterize the generator A of an exponentially bounded α-times integrated C-semigroup, either in terms of its Laplace transforms or in terms of existence of a unique solution of the above abstract Cauchy problem for every x...

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.

alpha-times Integrated Semigroups (alpha in R-)

Milorad Mijatović, Stevan Pilipović (1997)

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Nonlinear perturbations of analytical semigroups.

S. Oharu (1991)

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