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Integrated version of the Post-Widder inversion formula for Laplace transforms

José E. GaléMaría M. MartínezPedro J. Miana — 2011

Studia Mathematica

We establish an inversion formula of Post-Widder type for λ α -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.

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