Compactness properties of Feller semigroups

G. Metafune; D. Pallara; M. Wacker

Displaying similar documents to “Compactness properties of Feller 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....

On semigroups of $σ$ -endomorphisms

Iwanik, Anzelm

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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.

$𝒯$ -Prime Subsets in Semigroups

Bedřich Pondělíček (1975)

Matematický časopis

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Generation of analytic semigroups by elliptic operators of second order in Hölder spaces

Sergio Campanato (1980)

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

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Nella presente nota si comunica il seguente risultato: Un operatore ellittico del secondo ordine, con condizione di Dirichlet al bordo, è generatore infinitesimale di un semigruppo analitico in $t$ con la topologia degli spazi Hölderiani. La dimostrazione sarà esposta nel lavoro [2].

On a probabilistic problem on finite semigroups

Attila Nagy, Csaba Tóth (2023)

Commentationes Mathematicae Universitatis Carolinae

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We deal with the following problem: how does the structure of a finite semigroup $S$ depend on the probability that two elements selected at random from $S$ , with replacement, define the same inner right translation of $S$ . We solve a subcase of this problem. As the main result of the paper, we show how to construct not necessarily finite medial semigroups in which the index of the kernel of the right regular representation equals two.

Analytic semigroups on vector valued noncommutative $L^{p}$ -spaces

Cédric Arhancet (2013)

Studia Mathematica

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We give sufficient conditions on an operator space E and on a semigroup of operators on a von Neumann algebra M to obtain a bounded analytic or R-analytic semigroup ( ${(T \otimes I d_{E})}_{t \geq 0}$ on the vector valued noncommutative $L^{p}$ -space $L^{p} (M, E)$ . Moreover, we give applications to the $H^{\infty} (Σ_{θ})$ functional calculus of the generators of these semigroups, generalizing some earlier work of M. Junge, C. Le Merdy and Q. Xu.

On the positivity of semigroups of operators

Roland Lemmert, Peter Volkmann (1998)

Commentationes Mathematicae Universitatis Carolinae

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In a Banach space $E$ , let $U (t)$ $(t > 0)$ be a $C_{0}$ -semigroup with generating operator $A$ . For a cone $K \subseteq E$ with non-empty interior we show: $(☆)$ $U (t) [K] \subseteq K$ $(t > 0)$ holds if and only if $A$ is quasimonotone increasing with respect to $K$ . On the other hand, if $A$ is not continuous, then there exists a regular cone $K \subseteq E$ such that $A$ is quasimonotone increasing, but $(☆)$ does not hold.

Converging semigroups of holomorphic maps

Marco Abate (1988)

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

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In this paper we study the semigroups $\Phi:\mathbb{R}^{+}\rightarrow Hol(D,D)$ of holomorphic maps of a strictly convex domain $D\subset\mathbf{C}^{n}$ into itself. In particular, we characterize the semigroups converging, uniformly on compact subsets, to a holomorphic map $h:D\rightarrow\mathbf{C}^{n}$ .

Inverses of generators of nonanalytic semigroups

Ralph deLaubenfels (2009)

Studia Mathematica

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Suppose A is an injective linear operator on a Banach space that generates a uniformly bounded strongly continuous semigroup ${e^{t A}}_{t \geq 0}$ . It is shown that $A^{- 1}$ generates an $O (1 + τ) A {(1 - A)}^{- 1}$ -regularized semigroup. Several equivalences for $A^{- 1}$ generating a strongly continuous semigroup are given. These are used to generate sufficient conditions on the growth of ${e^{t A}}_{t \geq 0}$ , on subspaces, for $A^{- 1}$ generating a strongly continuous semigroup, and to show that the inverse of -d/dx on the closure of its image in L¹([0,∞)) does not generate...