We introduce a Laplace transform for Laplace hyperfunctions valued in a complete locally convex space $X$. In this general case the Laplace transform is a compatible family of holomorphic functions with values in local Banach spaces. Especially interesting is the case where $X=L_b(E,F)$ is the space of operators between locally convex spaces. In the forthcoming paper [6] this will be applied to solve the abstract Cauchy problem for operators in
complete ultrabornological locally convex spaces (like spaces of smooth functions and distributions) extending results of Komatsu for operators in Banach spaces.
@article{1291903394,
author = {Doma\'nski, Pawe\l\ and Langenbruch, Michael},
title = {On the Laplace transform for vector valued hyperfunctions},
journal = {Funct. Approx. Comment. Math.},
volume = {42},
number = {1},
year = {2010},
pages = { 129-159},
language = {en},
url = {http://dml.mathdoc.fr/item/1291903394}
}
Domański, Paweł; Langenbruch, Michael. On the Laplace transform for vector valued hyperfunctions. Funct. Approx. Comment. Math., Tome 42 (2010) no. 1, pp. 129-159. http://gdmltest.u-ga.fr/item/1291903394/