Almost periodic and strongly stable semigroups of operators

Vũ Phóng

Displaying similar documents to “Almost periodic and strongly stable semigroups of operators”

On the exponential stability and dichotomy of $C_{0}$ -semigroups

Phóng Vũ (1999)

Studia Mathematica

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A characterization of exponentially dichotomic and exponentially stable $C_{0}$ -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.

Asymptotic almost periodicity of $C$ -semigroups.

Xie, Linghong, Li, Miao, Huang, Falun (2003)

International Journal of Mathematics and Mathematical Sciences

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Spectral properties of weakly asymptotically almost periodic semigroups in the sense of Stepanov

Valentina Casarino (1997)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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The spectral structure of the infinitesimal generator of strongly measurable, asymptotically $S^{p}$ -almost periodic semigroups is investigated.

A quantitative asymptotic theorem for contraction semigroups with countable unitary spectrum

Charles Batty, Zdzisław Brzeźniak, David Greenfield (1996)

Studia Mathematica

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Let T be a semigroup of linear contractions on a Banach space X, and let $X_{s} (T) = x \in X : l i m_{s \to \infty} ∥ T (s) x ∥ = 0$ . Then $X_{s} (T)$ is the annihilator of the bounded trajectories of T*. If the unitary spectrum of T is countable, then $X_{s} (T)$ is the annihilator of the unitary eigenvectors of T*, and $l i m_{s} ∥ T (s) x ∥ = i n f ∥ x - y ∥ : y \in X_{s} (T)$ for each x in X.

Almost periodicity of C-semigroups, integrated semigroups and C-cosine functions

Xiaohui Gu, Miao Li, Falun Huang (2002)

Studia Mathematica

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We investigate the characterization of almost periodic C-semigroups, via the Hille-Yosida space Z₀, in case of R(C) being non-dense. Analogous results are obtained for C-cosine functions. We also discuss the almost periodicity of integrated semigroups.