In this article we describe properties of unbounded operators related to evolutionary problems. It is a survey article which also contains several new results. For instance we give a characterization of cosine functions in terms of mild well-posedness of the Cauchy problem of order 2, and we show that the property of having a bounded -calculus is stable under rank-1 perturbations whereas the property of being associated with a closed form and the property of generating a cosine function are not.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc75-0-2,
author = {Wolfgang Arendt and Charles J. K. Batty},
title = {Forms, functional calculus, cosine functions and perturbation},
journal = {Banach Center Publications},
volume = {75},
year = {2007},
pages = {17-38},
zbl = {1128.47021},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc75-0-2}
}
Wolfgang Arendt; Charles J. K. Batty. Forms, functional calculus, cosine functions and perturbation. Banach Center Publications, Tome 75 (2007) pp. 17-38. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc75-0-2/