Forms, functional calculus, cosine functions and perturbation

• Autorzy: Wolfgang Arendt , Charles J. K. Batty
• Języki publikacji: EN

Abstrakty

EN

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 $H^∞$-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.

Kategorie tematyczne

• 47D09: Operator sine and cosine functions and higher-order Cauchy problems
• 47A07: Forms (bilinear, sesquilinear, multilinear)
• 35L90: Abstract hyperbolic equations
• 47A60: Functional calculus

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2007
• Tom: 75
• Numer: 1
• Strony: 17-38

Daty

wydano

2007

Twórcy

autor

Wolfgang Arendt

• Abteilung Angewandte Analysis, Universität Ulm, 89069 Ulm, Germany

autor

Charles J. K. Batty

• St. John's College, Oxford OX1 3JP, U.K

Identyfikatory

DOI

10.4064/bc75-0-2