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Type: Journal article
Title: A generalization of the Widder-Arendt theorem
Author: Chojnacki, W.
Citation: Proceedings of the Edinburgh Mathematical Society, 2002; 45(1):161-179
Publisher: Oxford Univ Press
Issue Date: 2002
ISSN: 0013-0915
Statement of
Wojciech Chojnacki
Abstract: We establish a generalization of the Widder–Arendt theorem from Laplace transform theory. Given a Banach space E, a non-negative Borel measure m on the set R+ of all non-negative numbers, and an element ω of R∪{−∞} such that −λ is m-integrable for all λ > ω, where −λ is defined by −λ(t) = exp(−λt) for all t ∈ R+, our generalization gives an intrinsic description of functions r: (ω,∞) → E that can be represented as r(λ) = T( −λ) for some bounded linear operator T : L1(R+,m) → E and all λ > ω; here L1(R+,m) denotes the Lebesgue space based on m. We use this result to characterize pseudo-resolvents with values in a Banach algebra, satisfying a growth condition of Hille–Yosida type.
Keywords: Laplace–Stieltjes transform; weighted convolution algebra; representation; pseudo-resolvent; one-parameter semi
Provenance: Published online by Cambridge University Press 05 Feb 2002
Rights: Copyright © 2002 Edinburgh Mathematical Society
RMID: 0020021391
DOI: 10.1017/S0013091599000814
Appears in Collections:Computer Science publications

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