A class of evolution operators is introduced according to the device of Kato. An evolution operator introduced here provides a classical solution of the linear equation u'(t) = A(t)u(t) for t ∈ [0,T], in a general Banach space. The paper presents a necessary and sufficient condition for the existence and uniqueness of such an evolution operator.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm146-3-5,
author = {Naoki Tanaka},
title = {A characterization of evolution operators},
journal = {Studia Mathematica},
volume = {147},
year = {2001},
pages = {285-299},
zbl = {0980.47036},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm146-3-5}
}
Naoki Tanaka. A characterization of evolution operators. Studia Mathematica, Tome 147 (2001) pp. 285-299. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm146-3-5/