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

Jan Kisyński

Displaying similar documents to “Around Widder’s characterization of the Laplace transform of an element of $L^{\infty} (ℝ^{+})$ ”

Gelfand transform for a Boehmian space of analytic functions

V. Karunakaran, R. Angeline Chella Rajathi (2011)

Annales Polonici Mathematici

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Let $H^{\infty} ()$ denote the usual commutative Banach algebra of bounded analytic functions on the open unit disc of the finite complex plane, under Hadamard product of power series. We construct a Boehmian space which includes the Banach algebra A where A is the commutative Banach algebra with unit containing $H^{\infty} ()$ . The Gelfand transform theory is extended to this setup along with the usual classical properties. The image is also a Boehmian space which includes the Banach algebra C(Δ) of continuous...

Norm continuity of $c_{0}$ -semigroups

V. Goersmeyer, L. Weis (1999)

Studia Mathematica

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We show that a positive semigroup $T_{t}$ on $L_{p} (Ω, ν)$ with generator A and ||R(α + i β)|| → 0 as |β| → ∞ for some α ∈ ℝ is continuous in the operator norm for t>0. The proof is based on a criterion for norm continuity in terms of “smoothing properties” of certain convolution operators on general Banach spaces and an extrapolation result for the $L_{p}$ -scale, which may be of independent interest.

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 ergodicity for operators with bounded resolvent in Banach spaces

Kirsti Mattila (2011)

Studia Mathematica

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We prove results on ergodicity, i.e. on the property that the space is a direct sum of the kernel of an operator and the closure of its range, for closed linear operators A such that ${| | α (α - A)}^{- 1} | |$ is uniformly bounded for all α > 0. We consider operators on Banach spaces which have the property that the space is complemented in its second dual space by a projection P. Results on ergodicity are obtained under a norm condition ||I - 2P|| ||I - Q|| < 2 where Q is a projection depending on the...

Integrated version of the Post-Widder inversion formula for Laplace transforms

José E. Galé, María M. Martínez, Pedro J. Miana (2011)

Studia Mathematica

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We establish an inversion formula of Post-Widder type for $λ^{α}$ -multiplied vector-valued Laplace transforms (α > 0). This result implies an inversion theorem for resolvents of generators of α-times integrated families (semigroups and cosine functions) which, in particular, provides a unified proof of previously known inversion formulae for α-times integrated semigroups.

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.

Spectral mapping inclusions for the Phillips functional calculus in Banach spaces and algebras

Eva Fašangová, Pedro J. Miana (2005)

Studia Mathematica

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We investigate the weak spectral mapping property (WSMP) $\bar{μ ̂ (σ (A))} = σ (μ ̂ (A))$ , where A is the generator of a ₀-semigroup in a Banach space X, μ is a measure, and μ̂(A) is defined by the Phillips functional calculus. We consider the special case when X is a Banach algebra and the operators $e^{A t}$ , t ≥ 0, are multipliers.

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.

Transitivity for linear operators on a Banach space

Bertram Yood (1999)

Studia Mathematica

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Let G be the multiplicative group of invertible elements of E(X), the algebra of all bounded linear operators on a Banach space X. In 1945 Mackey showed that if $x_{1}, \dots, x_{n}$ and $y_{1}, \dots, y_{n}$ are any two sets of linearly independent elements of X with the same number of items, then there exists T ∈ G so that $T (x_{k}) = y_{k}$ , $k = 1, \dots, n$ . We prove that some proper multiplicative subgroups of G have this property.

Distributional {D}unkl transform and {D}unkl convolution operators

Jorge J. Betancor (2006)

Bollettino dell'Unione Matematica Italiana

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In this paper, that is divided in two parts, we study the distributional Dunkl transform on R. In the first part we investigate the Dunkl transform and the Dunkl convolution operators on tempered distributions. We prove that the tempered distributions defining Dunkl convolution operators on the Schwartz space are the elements of $\mathcal{O}^{\prime}_{c}$ , the space of usual convolution operators on $S$ . In the second part we define the distributional Dunkl transform by employing the kernel method. We introduce...

Noncommutative extensions of the Fourier transform and its logarithm

Romuald Lenczewski (2002)

Studia Mathematica

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We introduce noncommutative extensions of the Fourier transform of probability measures and its logarithm to the algebra (S) of complex-valued functions on the free semigroup S = FS(z,w) on two generators. First, to given probability measures μ, ν with all moments finite, we associate states μ̂, ν̂ on the unital free *-bialgebra (ℬ,ε,Δ) on two self-adjoint generators X,X’ and a projection P. Then we introduce and study cumulants which are additive under the convolution μ̂* ν̂ = μ̂ ⊗...

Factorization of vector measures and their integration operators

José Rodríguez (2016)

Colloquium Mathematicae

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Let X be a Banach space and ν a countably additive X-valued measure defined on a σ-algebra. We discuss some generation properties of the Banach space L¹(ν) and its connection with uniform Eberlein compacta. In this way, we provide a new proof that L¹(ν) is weakly compactly generated and embeds isomorphically into a Hilbert generated Banach space. The Davis-Figiel-Johnson-Pełczyński factorization of the integration operator $I_{ν} : L ¹ (ν) \to X$ is also analyzed. As a result, we prove that if $I_{ν}$ is both completely...

Displaying similar documents to “Around Widder’s characterization of the Laplace transform of an element of L ∞ ( ℝ + ) ”

Displaying similar documents to “Around Widder’s characterization of the Laplace transform of an element of $L^{\infty} (ℝ^{+})$ ”