Dynamics of weighted composition operators on weighted Banach spaces of entire functions
| Autor: | María José Beltrán-Meneu |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Composition operator Applied Mathematics Entire function 010102 general mathematics Banach space 01 natural sciences hypercyclic operator 010101 applied mathematics Multiplier (Fourier analysis) power bounded operator Operator (computer programming) Compact space weighted composition operator Bounded function weighted Banach spaces of entire functions mean ergodic operator Ergodic theory 0101 mathematics Analysis Mathematics |
| Zdroj: | Repositori Universitat Jaume I Universitat Jaume I |
| Popis: | We study the dynamics of the weighted composition operator C w , φ on weighted Banach spaces of entire functions H v ( C ) and H v 0 ( C ) . We characterize the continuity and compactness of the operator and, in the case of affine symbols φ ( z ) = a z + 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 λ C φ 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 H v 0 ( C ) is provided. For the case of composition operators, we obtain the spectrum and a complete characterization of the dynamics. |
| Databáze: | OpenAIRE |
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