Displaying similar documents to “The existence of the potential operator associated with an equicontinuous semigroup of class ( C 0 )

On a vector-valued local ergodic theorem in L

Ryotaro Sato (1999)

Studia Mathematica

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Let T = T ( u ) : u d + be a strongly continuous d-dimensional semigroup of linear contractions on L 1 ( ( Ω , Σ , μ ) ; X ) , where (Ω,Σ,μ) is a σ-finite measure space and X is a reflexive Banach space. Since L 1 ( ( Ω , Σ , μ ) ; X ) * = L ( ( Ω , Σ , μ ) ; X * ) , the adjoint semigroup T * = T * ( u ) : u d + becomes a weak*-continuous semigroup of linear contractions acting on L ( ( Ω , Σ , μ ) ; X * ) . In this paper the local ergodic theorem is studied for the adjoint semigroup T*. Assuming that each T(u), u d + , has a contraction majorant P(u) defined on L 1 ( ( Ω , Σ , μ ) ; ) , that is, P(u) is a positive linear contraction on L 1 ( ( Ω , Σ , μ ) ; ) such that T ( u ) f ( ω ) P ( u ) f ( · ) ( ω ) almost...

Semiflows and semigroups

Edoardo Vesentini (1996)

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

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Given a compact Hausdorff space K and a strongly continuous semigroup T of linear isometries of the Banach space of all complex-valued, continuous functions on K , the semiflow induced by T on K is investigated. In the particular case in which K is a compact, connected, differentiable manifold, a class of semigroups T preserving the differentiable structure of K is characterized.

On differences of heat semigroups

J. A. Van Casteren, M. Demuth (1989)

Annales scientifiques de l'Université de Clermont-Ferrand 2. Série Probabilités et applications

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Is A - 1 an infinitesimal generator?

Hans Zwart (2007)

Banach Center Publications

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In this paper we study the question whether A - 1 is the infinitesimal generator of a bounded C₀-semigroup if A generates a bounded C₀-semigroup. If the semigroup generated by A is analytic and sectorially bounded, then the same holds for the semigroup generated by A - 1 . However, we construct a contraction semigroup with growth bound minus infinity for which A - 1 does not generate a bounded semigroup. Using this example we construct an infinitesimal generator of a bounded semigroup for which its...

A complete description of dynamics generated by birth-and-death problem: a semigroup approach

Jacek Banasiak (2003)

Banach Center Publications

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We shall present necessary and sufficient conditions for both conservativity and uniqueness of solutions to birth-and-death system of equations using methods of semigroup theory. The derived conditions correspond to the uniqueness criteria for forward and backward birth-and-death systems due to Reuter, [10,11,1], that were derived in a different context by Markov processes' techniques.

Fractional powers of operators, K-functionals, Ulyanov inequalities

Walter Trebels, Ursula Westphal (2010)

Banach Center Publications

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Given an equibounded (₀)-semigroup of linear operators with generator A on a Banach space X, a functional calculus, due to L. Schwartz, is briefly sketched to explain fractional powers of A. Then the (modified) K-functional with respect to ( X , D ( ( - A ) α ) ) , α > 0, is characterized via the associated resolvent R(λ;A). Under the assumption that the resolvent satisfies a Nikolskii type inequality, | | λ R ( λ ; A ) f | | Y c φ ( 1 / λ ) | | f | | X , for a suitable Banach space Y, an Ulyanov inequality is derived. This will be of interest if one has...