Norm continuity of $c_0$-semigroups

V. Goersmeyer; L. Weis

Displaying similar documents to “Norm continuity of $c_{0}$ -semigroups”

On the stability of strongly continuous semigroups of positive operators on $L^{2} (μ)$

G. Greiner, R. Nagel (1983)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Regularized semigroups and systems of linear partial differential equations

M. Hieber, A. Holderrieth, F. Neubrander (1992)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Around Widder’s characterization of the Laplace transform of an element of $L^{\infty} (ℝ^{+})$

Jan Kisyński (2000)

Annales Polonici Mathematici

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Let ϰ be a positive, continuous, submultiplicative function on $ℝ^{+}$ such that $l i m_{t \to \infty} e^{- ω t} t^{- α} ϰ (t) = a$ for some ω ∈ ℝ, α ∈ $\bar{ℝ^{+}}$ and $a \in ℝ^{+}$ . For every λ ∈ (ω,∞) let $ϕ_{λ} (t) = e^{- λ t}$ for $t \in ℝ^{+}$ . Let $L_{ϰ}^{1} (ℝ^{+})$ be the space of functions Lebesgue integrable on $ℝ^{+}$ with weight $ϰ$ , and let E be a Banach space. Consider the map $ϕ_{•} : (ω, \infty) ∋ λ \to ϕ_{λ} \in L_{ϰ}^{1} (ℝ^{+})$ . Theorem 5.1 of the present paper characterizes the range of the linear map $T \to T ϕ_{•}$ defined on $L (L_{ϰ}^{1} (ℝ^{+}); E)$ , generalizing a result established by B. Hennig and F. Neubrander for $ϰ (t) = e^{ω t}$ . If ϰ ≡ 1 and E =ℝ then Theorem 5.1 reduces to D. V. Widder’s characterization...

A note on the spectral operators of scalar type and semigroups of bounded linear operators.

Markin, Marat V. (2002)

International Journal of Mathematics and Mathematical Sciences

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Functional calculi, regularized semigroups and integrated semigroups

Ralph deLaubenfels, Mustapha Jazar (1999)

Studia Mathematica

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We characterize closed linear operators A, on a Banach space, for which the corresponding abstract Cauchy problem has a unique polynomially bounded solution for all initial data in the domain of $A^{n}$ , for some nonnegative integer n, in terms of functional calculi, regularized semigroups, integrated semigroups and the growth of the resolvent in the right half-plane. We construct a semigroup analogue of a spectral distribution for such operators, and an extended functional calculus: When...

Unbounded well-bounded operators, strongly continuous semigroups and the Laplace transform

Ralph deLaubenfels (1992)

Studia Mathematica

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Suppose A is a (possibly unbounded) linear operator on a Banach space. We show that the following are equivalent. (1) A is well-bounded on [0,∞). (2) -A generates a strongly continuous semigroup ${e^{- s A}}_{s \leq 0}$ such that ${(1 / s^{2}) e^{- s A}}_{s > 0}$ is the Laplace transform of a Lipschitz continuous family of operators that vanishes at 0. (3) -A generates a strongly continuous differentiable semigroup ${e^{- s A}}_{s \geq 0}$ and ∃ M < ∞ such that $∥ H_{n} (s) ∥ \equiv ∥ (\sum_{k = 0}^{n} (s^{k} A^{k}) / k!) e^{- s A} ∥ \leq M$ , ∀s > 0, n ∈ ℕ ∪ 0. (4) -A generates a strongly continuous holomorphic semigroup ${e^{- z A}}_{R e (z) > 0}$ that is O(|z|)...

On resolvent positive operators and positive C0-semigroups on AL-spaces.

Jürgen Voigt (1989)

Semigroup forum

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Integrated semigroups of unbounded linear operators -- Cauchy problem. II.

Kravarušić, Ratko, Mijatović, Milorad, Pilipović, Stevan (1998)

Novi Sad Journal of Mathematics

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Displaying similar documents to “Norm continuity of c 0 -semigroups”

Displaying similar documents to “Norm continuity of $c_{0}$ -semigroups”