In this article we characterize the cyclicity of bounded composition operators $C_\phi f=f\circ \phi $ on the Paley–Wiener spaces of entire functions $B^2_\sigma $ for $\sigma >0$. We show that $C_\phi $ is cyclic precisely when $\phi (z)=z+b$ where either $b\in \mathbb{C}\setminus \mathbb{R}$ or...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Académie des sciences
2025-07-01
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| Series: | Comptes Rendus. Mathématique |
| Subjects: | |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.765/ |
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| Summary: | In this article we characterize the cyclicity of bounded composition operators $C_\phi f=f\circ \phi $ on the Paley–Wiener spaces of entire functions $B^2_\sigma $ for $\sigma >0$. We show that $C_\phi $ is cyclic precisely when $\phi (z)=z+b$ where either $b\in \mathbb{C}\setminus \mathbb{R}$ or $b\in \mathbb{R}$ with $0<\vert b \vert \le \pi /\sigma $. We also describe when the reproducing kernels of $B^2_\sigma $ are cyclic vectors for $C_\phi $ and see that this is related to a question of completeness of exponential sequences in $L^2[-\sigma ,\sigma ]$. The interplay between cyclicity and complex symmetry plays a key role in this work. |
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| ISSN: | 1778-3569 |