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

José E. Galé, María M. Martínez, and Pedro J. Miana. "Integrated version of the Post-Widder inversion formula for Laplace transforms." Studia Mathematica 206.2 (2011): 161-173. <http://eudml.org/doc/285880>.

@article{JoséE2011,
abstract = {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.},
author = {José E. Galé, María M. Martínez, Pedro J. Miana},
journal = {Studia Mathematica},
keywords = {Laplace transform; Post-Widder inversion formula; semigroups; cosine function},
language = {eng},
number = {2},
pages = {161-173},
title = {Integrated version of the Post-Widder inversion formula for Laplace transforms},
url = {http://eudml.org/doc/285880},
volume = {206},
year = {2011},
}

TY - JOUR
AU - José E. Galé
AU - María M. Martínez
AU - Pedro J. Miana
TI - Integrated version of the Post-Widder inversion formula for Laplace transforms
JO - Studia Mathematica
PY - 2011
VL - 206
IS - 2
SP - 161
EP - 173
AB - 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.
LA - eng
KW - Laplace transform; Post-Widder inversion formula; semigroups; cosine function
UR - http://eudml.org/doc/285880
ER -