Integrated version of the Post–Widder inversion formula for Laplace transforms
Volume 206 / 2011
Studia Mathematica 206 (2011), 161-173
MSC: Primary 44A10; Secondary 47D62.
DOI: 10.4064/sm206-2-4
Abstract
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.
