Weighted composition operators on Fock spaces and their dynamics

Tom Carroll; Clifford Gilmore

doi:10.1016/j.jmaa.2021.125234

Weighted composition operators on Fock spaces and their dynamics

Tom Carroll
, Clifford Gilmore

School of Mathematical Sciences

University College Cork

Research output: Contribution to journal › Article › peer-review

Abstract

Bounded weighted composition operators, as well as compact weighted composition operators, on Fock spaces have been characterised. This characterisation is refined in terms of the order and type of the multiplier, and a complete description of zero-free multipliers is obtained. Explicit asymptotics for iterates of such operators are given. As an application, the question of whether weighted composition operators on the Fock space can be supercyclic is answered in the negative.

Original language	English
Article number	125234
Journal	Journal of Mathematical Analysis and Applications
Volume	502
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2021.125234
Publication status	Published - 1 Oct 2021

Keywords

Boundedness
Compactness
Fock spaces
Linear dynamics
Supercyclic
Weighted composition operators

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10.1016/j.jmaa.2021.125234

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abstract = "Bounded weighted composition operators, as well as compact weighted composition operators, on Fock spaces have been characterised. This characterisation is refined in terms of the order and type of the multiplier, and a complete description of zero-free multipliers is obtained. Explicit asymptotics for iterates of such operators are given. As an application, the question of whether weighted composition operators on the Fock space can be supercyclic is answered in the negative.",

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AB - Bounded weighted composition operators, as well as compact weighted composition operators, on Fock spaces have been characterised. This characterisation is refined in terms of the order and type of the multiplier, and a complete description of zero-free multipliers is obtained. Explicit asymptotics for iterates of such operators are given. As an application, the question of whether weighted composition operators on the Fock space can be supercyclic is answered in the negative.

KW - Boundedness

KW - Compactness

KW - Fock spaces

KW - Linear dynamics

KW - Supercyclic

KW - Weighted composition operators

UR - https://www.scopus.com/pages/publications/85104779628

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Weighted composition operators on Fock spaces and their dynamics

Abstract

Keywords

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