The Laplace transform of analytic vector-valued functions (real conditions)

Miroslav Sova

Displaying similar documents to “The Laplace transform of analytic vector-valued functions (real conditions)”

Relation between real and complex properties of the Laplace transform

Miroslav Sova (1980)

Časopis pro pěstování matematiky

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On a fundamental theorem of the Laplace transform theory

Miroslav Sova (1981)

Časopis pro pěstování matematiky

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Shilov parabolic systems

M. Kostić (2012)

Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques

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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...

On a class of second order integrodifferential equations

Daniela Sforza (1991)

Rendiconti del Seminario Matematico della Università di Padova

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Displaying similar documents to “The Laplace transform of analytic vector-valued functions (real conditions)”

Relation between real and complex properties of the Laplace transform

On a fundamental theorem of the Laplace transform theory

Shilov parabolic systems

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

On a class of second order integrodifferential equations

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