Geodesic
Integrated version of the Post–Widder inversion formula for Laplace transforms
José E. Galé1 ; María M. Martínez1 ; Pedro J. Miana1
1 Departamento de Matemáticas e IUMA Universidad de Zaragoza 50009 Zaragoza, Spain
Studia Mathematica, Tome 206 (2011) no. 2, pp. 161-173

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We establish an inversion formula of Post–Widder type for $\lambda ^{\alpha }$-multiplied vector-valued Laplace transforms ($\alpha >0$). This result implies an inversion theorem for resolvents of generators of $\alpha $-times integrated families (semigroups and cosine functions) which, in particular, provides a unified proof of previously known inversion formulae for $\alpha $-times integrated semigroups.
DOI : 10.4064/sm206-2-4
Keywords: establish inversion formula post widder type lambda alpha multiplied vector valued laplace transforms alpha result implies inversion theorem resolvents generators alpha times integrated families semigroups cosine functions which particular provides unified proof previously known inversion formulae alpha times integrated semigroups

José E. Galé 1 ; María M. Martínez 1 ; Pedro J. Miana 1

1 Departamento de Matemáticas e IUMA Universidad de Zaragoza 50009 Zaragoza, Spain 
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 for Laplace transforms
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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 206 (2011) no. 2, pp. 161-173. doi: 10.4064/sm206-2-4

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