This paper is concerned with double families of evolution operators employed in the study of dynamical systems in which cause and effect are represented in different Banach spaces. The main tool is the Laplace transform of vector-valued functions. It is used to define the generator of the double family which is a pair of unbounded linear operators and relates to implicit evolution equations in a direct manner. The characterization of generators for a special class of evolutions is presented.
@article{bwmeta1.element.bwnjournal-article-bcpv38i1p325bwm,
author = {Sauer, Niko},
title = {Empathy theory and the Laplace transform},
journal = {Banach Center Publications},
volume = {38},
year = {1997},
pages = {325-338},
zbl = {0885.47013},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv38i1p325bwm}
}
Sauer, Niko. Empathy theory and the Laplace transform. Banach Center Publications, Tome 38 (1997) pp. 325-338. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv38i1p325bwm/
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