Displaying similar documents to “Frequently hypercyclic translation semigroups”

Classes of distribution semigroups

Peer Christian Kunstmann, Modrag Mijatović, Stevan Pilipović (2008)

Studia Mathematica

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We introduce various classes of distribution semigroups distinguished by their behavior at the origin. We relate them to quasi-distribution semigroups and integrated semigroups. A class of such semigroups, called strong distribution semigroups, is characterized through the value at the origin in the sense of Łojasiewicz. It contains smooth distribution semigroups as a subclass. Moreover, the analysis of the behavior at the origin involves intrinsic structural results for semigroups....

Compactness properties of Feller semigroups

G. Metafune, D. Pallara, M. Wacker (2002)

Studia Mathematica

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We study the compactness of Feller semigroups generated by second order elliptic partial differential operators with unbounded coefficients in spaces of continuous functions in ℝ N .

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...

Convergence at the origin of integrated semigroups

Vincent Cachia (2008)

Studia Mathematica

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We study a classification of κ-times integrated semigroups (for κ > 0) by their (uniform) rate of convergence at the origin: | | S ( t ) | | = ( t α ) as t → 0 (0 ≤ α ≤ κ). By an improved generation theorem we characterize this behaviour by Hille-Yosida type estimates. Then we consider integrated semigroups with holomorphic extension and characterize their convergence at the origin, as well as the existence of boundary values, by estimates of the associated holomorphic semigroup. Various examples illustrate...

C₀-semigroups generated by second order differential operators

Gabriela Raluca Mocanu (2016)

Annales Polonici Mathematici

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Let W ( u ) ( x ) = 1 / 2 x a ( 1 - x ) b u ' ' ( x ) with a,b ≥ 2. We consider the C₀-semigroups generated by this operator on the spaces of continuous functions, respectively square integrable functions. The connection between these semigroups together with suitable approximation processes is studied. Also, some qualitative and quantitative properties are derived.

The asymptotic behaviour of the counting functions of Ω-sets in arithmetical semigroups

Maciej Radziejewski (2014)

Acta Arithmetica

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We consider an axiomatically-defined class of arithmetical semigroups that we call simple L-semigroups. This class includes all generalized Hilbert semigroups, in particular the semigroup of non-zero integers in any algebraic number field. We show, for all positive integers k, that the counting function of the set of elements with at most k distinct factorization lengths in such a semigroup has oscillations of logarithmic frequency and size √ x ( l o g x ) - M for some M>0. More generally, we show...

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.

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.

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.

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...

Weighted convolution algebras on subsemigroups of the real line

H. G. Dales, H. V. Dedania

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In this memoir, we shall consider weighted convolution algebras on discrete groups and semigroups, concentrating on the group (ℚ,+) of rational numbers, the semigroup ( ℚ + • , + ) of strictly positive rational numbers, and analogous semigroups in the real line ℝ. In particular, we shall discuss when these algebras are Arens regular, when they are strongly Arens irregular, and when they are neither, giving a variety of examples. We introduce the notion of ’weakly diagonally bounded’ weights, weakening...

The Cesàro and related operators, a survey

V. G. Miller (2007)

Banach Center Publications

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We provide a survey of properties of the Cesàro operator on Hardy and weighted Bergman spaces, along with its connections to semigroups of weighted composition operators. We also describe recent developments regarding Cesàro-like operators and indicate some open questions and directions of future research.