# Publishing house / Banach Center Publications / All volumes

## 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.

#### Authors

• Wolfgang ArendtAbteilung Angewandte Analysis
Universität Ulm
89069 Ulm
Germany
e-mail
• Charles J. K. BattySt. John's College
Oxford OX1 3JP
U.K
e-mail

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