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

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

Studia Mathematica (2011)

- Volume: 206, Issue: 2, page 161-173
- ISSN: 0039-3223

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topJosé 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 -

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