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arXiv · 2411.01339

Cyclicity of composition operators on the Paley-Wiener spaces

Pham Viet Hai·Waleed Noor·Osmar Reis Severiano
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Abstract

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.

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Pham Viet Hai, Waleed Noor, Osmar Reis Severiano. 2025-05-09. Cyclicity of composition operators on the Paley-Wiener spaces. https://doi.org/10.5802/crmath.765

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