arXiv subjects

O. R. Severiano

Publications and source records attributed to O. R. Severiano.

3 recordsLinked to original sources

arXiv2026

Expansivity and shadowing for composition operators on Paley-Wiener spaces

In this article, we study composition operators $C_ϕf=f\circ ϕ$ on the full range of Paley-Wiener spaces $B^2_a$ for $a>0.$ Here we compute the spectrum and the spectral radius of $C_ϕ$ on $B^2_a.$ The spectrum of $C_ϕ$ and the location of the fixed point of $ϕ$ play a fundamental role in our analysis to show that no Paley-Wiener space $B^2_a$ supports composition operators possessing the positive shadowing property. We also provide a complete classification of the composition operators on $B^2_a$ that are positively expansive and absolutely Cesàro bounded. As a consequence of these results we show that no Paley-Wiener space $B^2_a$ supports Li-Yorke chaotic composition operators.

math.FA↗

arXiv2022

Complex symmetry of linear fractional composition operators on a half-plane

We investigate the bounded composition operators induced by linear fractional self-maps of the right half-plane $\mathbb{C}_+$ on the Hardy space $H^2(\mathbb{C}_+).$ We completely characterize which of these operators are cohyponormal and we find conjugations for the linear fractional composition operators that are complex symmetric.

math.FA↗

arXiv2022

Composition operators on Hardy-Smirnov spaces

We investigate composition operators $C_Φ$ on the Hardy-Smirnov space $H^{2}(Ω)$ induced by analytic self-maps $Φ$ of an open simply connected proper subset $Ω$ of the complex plane. When the Riemann map $τ:\mathbb{U}\rightarrowΩ$ used to define the norm of $H^{2}(Ω)$ is a linear fractional transformation, we characterize the composition operators whose adjoints are composition operators. As applications of this fact, we provide a new proof for the adjoint formula discovered by Gallardo-Gutiérrez and Montes-Rodríguez and we give a new approach to describe all Hermitian and unitary composition operators on $H^{2}(Ω).$ Additionally, if the coefficients of $τ$ are real, we exhibit concrete examples of conjugations and describe the Hermitian and unitary composition operators which are complex symmetric with respect to specific conjugations on $H^{2}(Ω).$ We finish this paper showing that if $Ω$ is unbounded and $Φ$ is a non-automorphic self-map of $Ω$ with a fixed point, then $C_Φ$ is never complex symmetric on $H^{2}(Ω).$

math.FA↗