Cyclicity of composition operators on the Paley-Wiener spaces
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866918084215832576 |
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| author | Hai, Pham Viet Noor, Waleed Severiano, Osmar Reis |
| author_facet | Hai, Pham Viet Noor, Waleed Severiano, Osmar Reis |
| contents | In this article we characterize the cyclicity of bounded composition operators $C_ϕf=f\circ ϕ$ on the Paley-Wiener spaces of entire functions $B^2_σ$ for $σ>0$. We show that $C_ϕ$ is cyclic precisely when $ϕ(z)=z+b$ where either $b\in\mathbb{C}\setminus\mathbb{R}$ or $b\in\mathbb{R}$ with $0<|b|\leq π/σ$. We also describe when the reproducing kernels of $B^2_σ$ are cyclic vectors for $C_ϕ$ and see that this is related to a question of completeness of exponential sequences in $L^2[-σ,σ]$. The interplay between cyclicity and complex symmetry plays a key role in this work. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_01339 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cyclicity of composition operators on the Paley-Wiener spaces Hai, Pham Viet Noor, Waleed Severiano, Osmar Reis Functional Analysis In this article we characterize the cyclicity of bounded composition operators $C_ϕf=f\circ ϕ$ on the Paley-Wiener spaces of entire functions $B^2_σ$ for $σ>0$. We show that $C_ϕ$ is cyclic precisely when $ϕ(z)=z+b$ where either $b\in\mathbb{C}\setminus\mathbb{R}$ or $b\in\mathbb{R}$ with $0<|b|\leq π/σ$. We also describe when the reproducing kernels of $B^2_σ$ are cyclic vectors for $C_ϕ$ and see that this is related to a question of completeness of exponential sequences in $L^2[-σ,σ]$. The interplay between cyclicity and complex symmetry plays a key role in this work. |
| title | Cyclicity of composition operators on the Paley-Wiener spaces |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2411.01339 |