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Zbl 0637.44001
Arendt, Wolfgang
Vector-valued Laplace transforms and Cauchy problems. (English)
[J] Isr. J. Math. 59, 327-352 (1987). ISSN 0021-2172; ISSN 1565-8511/e

The author symmetrically treats linear differential equations in Banach spaces with the help of Laplace transforms. The central tool used is an ``integrated version'' of Widder's theorem (characterising Laplace transforms of bounded functions). It holds in any Banach space, whereas the vector-valued version of Widder's theorem itself holds if and only if the Banach space has the Radon - Nikodým property. The Hille-Yosida theorem and other generation theorems are immediate consequences. The technique presented in the paper can be applied to operators whose domains are not dense.
[S.D.Bajpai]

MSC 2000:: *44A10 Laplace transform
34G10 Linear ODE in abstract spaces
47D03 (Semi)groups of linear operators

Keywords: one-parameter semigroups of operators; Banach spaces; Laplace transforms; Radon - Nikodým property; Hille-Yosida theorem

Cited in: Zbl 1154.47035 Zbl 1113.60078 Zbl 1018.44002 Zbl 0964.44001 Zbl 0983.34051 Zbl 0999.47030 Zbl 0832.47032 Zbl 0783.47057 Zbl 0762.47013 Zbl 0746.47019 Zbl 0741.34040 Zbl 0702.47028 Zbl 0683.47027

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