This paper is concerned with the problem of real characterization of locally Lipschitz continuous (n + 1)-times integrated semigroups, where n is a nonnegative integer. It is shown that a linear operator is the generator of such an integrated semigroup if and only if it is closed, its resolvent set contains all sufficiently large real numbers, and a stability condition in the spirit of the finite difference approximation theory is satisfied.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm167-1-1,
author = {Naoki Tanaka},
title = {Locally Lipschitz continuous integrated semigroups},
journal = {Studia Mathematica},
volume = {166},
year = {2005},
pages = {1-16},
zbl = {1068.47053},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm167-1-1}
}
Naoki Tanaka. Locally Lipschitz continuous integrated semigroups. Studia Mathematica, Tome 166 (2005) pp. 1-16. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm167-1-1/