Cyclicity of composition operators on the Paley-Wiener spaces
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.
math.FA↗