On the stability of degenerate difference systems in Banach spaces
โ Scribed by M. Benabdallakh; A. G. Rutkas; A. A. Solov'ev
- Publisher
- Springer US
- Year
- 1991
- Tongue
- English
- Weight
- 343 KB
- Volume
- 57
- Category
- Article
- ISSN
- 1573-8795
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๐ SIMILAR VOLUMES
The paper is devoted to some results on the problem of S. M. Ulam for the stability of functional equations in Banach spaces. The problem was posed by Ulam 60 years ago.
The main aim of this work is to define and exemplify various stability concepts and to emphasize connections between them. These stability concepts are included in a general concept, the so-called (h, k)-stability. We motivate our approach with illustrative examples.
In this paper we investigate the strong asymptotic stability of linear dynamical systems in Banach spaces. Let \(\alpha\) be the infinitesimal generator of a \(C_{0}\)-semigroup \(e^{t i f f}\) of bounded linear operators in a Banach space \(X\). We first show that if \(e^{t . \alpha}\) is a \(C_{0}