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Bulletin of the Belgian Mathematical Society - Simon Stevin
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Bulletin of the Belgian Mathematical Society - Simon Stevin
Article . 2010 . Peer-reviewed
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https://dx.doi.org/10.36045/bb...
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An extension of a theorem of E. A. Barbashin to the dichotomy of abstract evolution operators

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Aug 2010Publisher:The Belgian Mathematical SocietyJournal:Bulletin of the Belgian Mathematical Society - Simon Stevin, volume 17 (issn: 1370-1444, Copyright policy )
Authors: Preda, Ciprian; Preda, Petre;

doi: 10.36045/bbms/1290608196

An extension of a theorem of E. A. Barbashin to the dichotomy of abstract evolution operators

Abstract

Using a discrete time method, the authors give a necessary and sufficient condition for the uniform exponential dichotomy for abstract evolution equations. This extends known results by Barbashin, Datko, Lovelady, Pazy and Preda.

Keywords

Dichotomy, trichotomy of solutions to ordinary differential equations, Linear differential equations in abstract spaces, One-parameter semigroups and linear evolution equations, evolution families, uniform exponential dichotomy, 34D05, 47D06

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    popularity
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    influence
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
4
Top 10%
Average
Average
Green
hybrid