If A is the generator of an exponentially bounded C-cosine function on a Ž . Banach space X, then the abstract Cauchy problem ACP for A has a unique Ž . Ž . y 1 Ž . solution for every pair x, y of initial values from y A C X . The main result is a characterization of the generator of a C-cosine func
On the Spectrum of Cosine Functions
✍ Scribed by Elena Schüler
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 138 KB
- Volume
- 229
- Category
- Article
- ISSN
- 0022-247X
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✦ Synopsis
In this paper we give characterizations of the resolvent set of the generator A of Ž . a strongly continuous cosine function C t in terms of certain solution properties Ž . Ž . Ž . of the differential equation uЉ t s Au t q f t .
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