A generalization of the Widder-Arendt theorem
| dc.contributor.author | Chojnacki, W. | |
| dc.date.issued | 2002 | |
| dc.description.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. | |
| dc.description.statementofresponsibility | Wojciech Chojnacki | |
| dc.identifier.citation | Proceedings of the Edinburgh Mathematical Society, 2002; 45(1):161-179 | |
| dc.identifier.doi | 10.1017/S0013091599000814 | |
| dc.identifier.issn | 0013-0915 | |
| dc.identifier.issn | 1464-3839 | |
| dc.identifier.orcid | Chojnacki, W. [0000-0001-7782-1956] | |
| dc.identifier.uri | http://hdl.handle.net/2440/1360 | |
| dc.language.iso | en | |
| dc.provenance | Published online by Cambridge University Press 05 Feb 2002 | |
| dc.publisher | Oxford Univ Press | |
| dc.rights | Copyright © 2002 Edinburgh Mathematical Society | |
| dc.source.uri | https://doi.org/10.1017/s0013091599000814 | |
| dc.subject | Laplace–Stieltjes transform | |
| dc.subject | weighted convolution algebra | |
| dc.subject | representation | |
| dc.subject | pseudo-resolvent | |
| dc.subject | one-parameter semi | |
| dc.title | A generalization of the Widder-Arendt theorem | |
| dc.type | Journal article | |
| pubs.publication-status | Published |
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