Displaying similar documents to “Semigroups of operators commuting with translations”

Hille-Yosida type theorems for local regularized semigroups and local integrated semigroups

Sheng Wang Wang (2002)

Studia Mathematica

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Motivated by a great deal of interest recently in operators that may not be densely defined, we deal with regularized semigroups and integrated semigroups that are either not exponentially bounded or not defined on [0,∞) and generated by closed operators which may not be densely defined. Some characterizations and related examples are presented. Our results are extensions of the corresponding results produced by other authors.

Frequently hypercyclic semigroups

Elisabetta M. Mangino, Alfredo Peris (2011)

Studia Mathematica

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We study frequent hypercyclicity in the context of strongly continuous semigroups of operators. More precisely, we give a criterion (sufficient condition) for a semigroup to be frequently hypercyclic, whose formulation depends on the Pettis integral. This criterion can be verified in certain cases in terms of the infinitesimal generator of the semigroup. Applications are given for semigroups generated by Ornstein-Uhlenbeck operators, and especially for translation semigroups on weighted...

Linear dynamics of semigroups generated by differential operators

J. Alberto Conejero, Carlos Lizama, Marina Murillo-Arcila, Alfredo Peris (2017)

Open Mathematics

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During the last years, several notions have been introduced for describing the dynamical behavior of linear operators on infinite-dimensional spaces, such as hypercyclicity, chaos in the sense of Devaney, chaos in the sense of Li-Yorke, subchaos, mixing and weakly mixing properties, and frequent hypercyclicity, among others. These notions have been extended, as far as possible, to the setting of C0-semigroups of linear and continuous operators. We will review some of these notions and...

Perturbations of bi-continuous semigroups

Bálint Farkas (2004)

Studia Mathematica

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The notion of bi-continuous semigroups has recently been introduced to handle semigroups on Banach spaces that are only strongly continuous for a topology coarser than the norm-topology. In this paper, as a continuation of the systematic treatment of such semigroups started in [20-22], we provide a bounded perturbation theorem, which turns out to be quite general in view of various examples.

Green's relations and their generalizations on semigroups

Kar-Ping Shum, Lan Du, Yuqi Guo (2010)

Discussiones Mathematicae - General Algebra and Applications

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Green's relations and their generalizations on semigroups are useful in studying regular semigroups and their generalizations. In this paper, we first give a brief survey of this topic. We then give some examples to illustrate some special properties of generalized Green's relations which are related to completely regular semigroups and abundant semigroups.

Perturbation theorems for local integrated semigroups and their applications

Sheng Wang Wang, Mei Ying Wang, Yan Shen (2005)

Studia Mathematica

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Motivated by a great deal of interest in operators that may not be densely defined and do not generate global integrated semigroups, we establish general perturbation theorems for local integrated semigroups and describe their applications to local complete second order abstract differential equations.