arXiv subjects
Publications and source records attributed to Artur Blois.
Let $ϕ$ be a holomorphic self-map of the open unit disk $\mathbb{D}.$ In this article, we study the shadowing phenomenon for composition operators $C_ϕf=f\circ ϕ$ on the Hardy space $H^2(\mathbb{D}).$ We mainly characterize all the composition operators induced by linear fractional self-maps of $\mathbb{D}$ that have the positive shadowing property.
In this article, we study cyclic phenomena on the full range of weighted Bergman spaces on the right half-plane $\mathcal{A}^{2}_α(\mathbb C_{+}).$ We completely characterize cyclic and supercyclic composition operators induced by affine self-maps of $\mathbb C_+,$ thereby completing the characterization of all hypercyclic, supercyclic and cyclic composition operators induced by affine symbols on $\mathcal{A}^{2}_α(\mathbb C_{+}).$
In this article, we completely characterize the positive expansive and absolutely Cesàro composition operators $C_ϕf=f\circ ϕ$ induced by affine self-maps $ϕ$ of the right half-plane $\mathbb{C}_+$ on the weighted Bergman space $\mathcal{A}^2_α(\mathbb{C}_+)$. Furthermore, we characterize which of these operators have the positive shadowing property.