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Complex Analysis and Operator Theory
Article . 2012 . Peer-reviewed
License: Springer TDM
Data sources: Crossref
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
zbMATH Open
Article . 2014
Data sources: zbMATH Open
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Dynamics of Weighted Composition Operators

Dynamics of weighted composition operators
Authors: Bes, Juan;

Dynamics of Weighted Composition Operators

Abstract

In the paper under review, the author is concerned with the dynamics of the weighted composition operator \(C_{\omega,\varphi}: H(\Omega)\to H(\Omega)\) given by \(C_{\omega,\varphi}(f)(z)=\omega(z)(f\circ \varphi)(z)\), for \(z\in \Omega\), where \(H(\Omega)\) denotes the space of holomorphic functions on a simply connected domain \(\Omega\) of the complex field, endowed with the compact open topology, \(\varphi\) is a holomorphic self map of \(\Omega\), and \(\omega\in H(\Omega)\). In particular, the author shows that any such operator \(C_{\omega,\varphi}\) is weakly supercyclic if and only if it is topologically mixing and, in the case that the weight is bounded, if and only if the operator has a hypercyclic subspace. The author also provides conditions on the symbol in order that the operator \(C_{\omega,\varphi}\) is Devaney-chaotic and has a frequently hypercyclic subspace.

Related Organizations
Keywords

chaotic operators, composition operators, Linear composition operators, Physical Sciences and Mathematics, Cyclic vectors, hypercyclic and chaotic operators, Compositional universality, supercyclic operators, hypercyclic operators

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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!
21
Top 10%
Top 10%
Average
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