A spectral mapping theorem for semigroups solving PDEs with nonautonomous past.
Fragnelli, Genni (2003)
Abstract and Applied Analysis
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Fragnelli, Genni (2003)
Abstract and Applied Analysis
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Yu Lyubich, Phóng Vũ (1988)
Studia Mathematica
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Fuensanta Andreu Vaíllo, José Manuel Mazón Ruiz (1990)
Publicacions Matemàtiques
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In this paper we get some relations between the boundary point spectrum of the generator A of a C-semigroup and the generator A* of the dual semigroup. This relations combined with the results due to Lyubich-Phong and Arendt-Batty, yield stability results on positive C-semigroups.
Yuri Tomilov (1999)
Studia Mathematica
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Some statements of the paper [4] are corrected.
Jaromír J. Koliha, Trung Dinh Tran (2003)
Czechoslovak Mathematical Journal
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We study a class of closed linear operators on a Banach space whose nonzero spectrum lies in the open left half plane, and for which is at most a simple pole of the operator resolvent. Our spectral theory based methods enable us to give a simple proof of the characterization of -semigroups of bounded linear operators with asynchronous exponential growth, and recover results of Thieme, Webb and van Neerven. The results are applied to the study of the asymptotic behavior of the solutions...
Vũ Phóng (1997)
Banach Center Publications
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This paper is chiefly a survey of results obtained in recent years on the asymptotic behaviour of semigroups of bounded linear operators on a Banach space. From our general point of view, discrete families of operators on a Banach space X (discrete one-parameter semigroups), one-parameter -semigroups on X (strongly continuous one-parameter semigroups), are particular cases of representations of topological abelian semigroups. Namely, given a topological abelian semigroup S, a family...
Rainer Nagel (1997)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Phóng Vũ (1999)
Studia Mathematica
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A characterization of exponentially dichotomic and exponentially stable -semigroups in terms of solutions of an operator equation of Lyapunov type is presented. As a corollary a new and shorter proof of van Neerven’s recent characterization of exponential stability in terms of boundedness of convolutions of a semigroup with almost periodic functions is given.