Integrated version of the Post-Widder inversion formula for Laplace transforms
José E. Galé ; María M. Martínez ; Pedro J. Miana
Studia Mathematica, Tome 204 (2011), p. 161-173 / Harvested from The Polish Digital Mathematics Library
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We establish an inversion formula of Post-Widder type for λα-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.

Publié le : 2011-01-01
EUDML-ID : urn:eudml:doc:285880 
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José E. Galé; María M. Martínez; Pedro J. Miana. Integrated version of the Post-Widder inversion formula for Laplace transforms. Studia Mathematica, Tome 204 (2011) pp. 161-173. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm206-2-4/