Dynamics of weighted composition operators on weighted Banach spaces of entire functions
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Title
Dynamics of weighted composition operators on weighted Banach spaces of entire functionsAuthor (s)
Date
2020-07-22Publisher
Elsevier; Academic PressISSN
0022-247XBibliographic citation
BELTRÁN-MENEU, María J. Dynamics of weighted composition operators on weighted Banach spaces of entire functions. Journal of Mathematical Analysis and Applications, 2020, vol. 492, no 1, p. 124422.Type
info:eu-repo/semantics/articlePublisher version
https://www.sciencedirect.com/journal/journal-of-mathematical-analysis-and-appli ...Version
info:eu-repo/semantics/acceptedVersionSubject
Abstract
We study the dynamics of the weighted composition operator Cw,ϕ on the weighted
Banach spaces of entire functions Hv(C) and H0
v
(C). We characterize the continuity
and compactness of the operator and, in the case ... [+]
We study the dynamics of the weighted composition operator Cw,ϕ on the weighted
Banach spaces of entire functions Hv(C) and H0
v
(C). We characterize the continuity
and compactness of the operator and, in the case of affine symbols ϕ(z) = az+b, a, b ∈
C, and exponential weights, we analyze when the operator is power bounded, (uniformly) mean ergodic and hypercyclic. Continuous weighted composition operators
when |a| = 1 are just multiples of composition operators λCϕ λ ∈ C. When |a| < 1,
we consider as a multiplier w the product of a polynomial by an exponential function.
For multiples of composition operators, we get a complete characterization of power
boundedness and mean ergodicity and we study the hypercyclicity in terms of λ. An
example of a power bounded but not mean ergodic operator on H0
v
(C) is provided.
For the case of composition operators, we obtain the spectrum and a complete characterization of the dynamics. [-]
Is part of
Journal of Mathematical Analysis and Applications Volume 492, Issue 1, 1 December 2020, 124422Investigation project
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info:eu-repo/semantics/openAccess
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