Forms, functional calculus, cosine functions and perturbation
Volume 75 / 2007
Banach Center Publications 75 (2007), 17-38
MSC: Primary 47A60; Secondary 35L90, 47A07, 47D09.
DOI: 10.4064/bc75-0-2
Abstract
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 $H^\infty$-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.
