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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Académie des sciences
2025-07-01
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| Series: | Comptes Rendus. Mathématique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.765/ |
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| author | Viet Hai, Pham Noor, Waleed Reis Severiano, Osmar |
| author_facet | Viet Hai, Pham Noor, Waleed Reis Severiano, Osmar |
| author_sort | Viet Hai, Pham |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-716992ffd46e48c8907ba919bbf10e1c |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-716992ffd46e48c8907ba919bbf10e1c2025-08-20T03:58:13ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692025-07-01363G987988610.5802/crmath.76510.5802/crmath.765Viet Hai, Pham0Noor, Waleed1Reis Severiano, Osmar2Faculty of Mathematics and Informatics, Hanoi University of Science and Technology, Khoa Toan-Tin, Dai hoc Bach khoa Hanoi, 1 Dai Co Viet, Hanoi, VietnamIMECC, Universidade Estadual de Campinas, Campinas-SP, BrazilIMECC, Universidade Estadual de Campinas, Campinas-SP, BrazilIn 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.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.765/Cyclic operatorcomposition operatorPaley–Wiener space |
| spellingShingle | Viet Hai, Pham Noor, Waleed Reis Severiano, Osmar Comptes Rendus. Mathématique Cyclic operator composition operator Paley–Wiener space |
| topic | Cyclic operator composition operator Paley–Wiener space |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.765/ |