An inequality concerning the growth bound of a discrete evolution family on a complex Banach space

Constantin Buşe; Donal O’Regan; Olivia Saierli

doi:10.1080/10236198.2016.1162160

An inequality concerning the growth bound of a discrete evolution family on a complex Banach space

Constantin Buşe
, Donal O’Regan
, Olivia Saierli

Mathematics

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

4 Citations (Scopus)

Abstract

We prove that the uniform growth bound ω₀(u) of a discrete evolution family (u) of bounded linear operators acting on a complex Banach space X satisfies the inequality ω₀(u)cu(X)≤–1; here cu(X) is the operator norm of a convolution operator which acts on a certain Banach space X of X-valued sequences.

Original language	English
Pages (from-to)	904-912
Number of pages	9
Journal	Journal of Difference Equations and Applications
Volume	22
Issue number	7
DOIs	https://doi.org/10.1080/10236198.2016.1162160
Publication status	Published - 2 Jul 2016

Keywords

Uniform exponential stability
convolution operator on sequence spaces
exponentially bounded evolution families of operators
growth bounds

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10.1080/10236198.2016.1162160

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abstract = "We prove that the uniform growth bound ω0(u) of a discrete evolution family (u) of bounded linear operators acting on a complex Banach space X satisfies the inequality ω0(u)cu(X)≤–1; here cu(X) is the operator norm of a convolution operator which acts on a certain Banach space X of X-valued sequences.",

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AB - We prove that the uniform growth bound ω0(u) of a discrete evolution family (u) of bounded linear operators acting on a complex Banach space X satisfies the inequality ω0(u)cu(X)≤–1; here cu(X) is the operator norm of a convolution operator which acts on a certain Banach space X of X-valued sequences.

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KW - convolution operator on sequence spaces

KW - exponentially bounded evolution families of operators

KW - growth bounds

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An inequality concerning the growth bound of a discrete evolution family on a complex Banach space

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Keywords

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