arXiv subjects
Publications and source records attributed to Osmar R. Severiano.
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 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.
In the paper, we investigate weighted composition operators on Bergman spaces of a half-plane. We characterize weighted composition operators which are hermitian and those which are complex symmetric with respect to a family of conjugations. As it turns out, weighted composition operators enhanced by a symmetry must be bounded. Hermitian, and unitary weighted composition operators are proven to be complex symmetric with respect to an adapted and highly relevant conjugation. We classify which the linear fractional functions give rise to the complex symmetry of bounded composition operators. We end the paper with a natural link to complex symmetry in Lebesgue space.
We investigate the relationship between the complex symmetry of composition operators $C_ϕf=f\circ ϕ$ induced on the classical Hardy space $H^2(\mathbb{D})$ by an analytic self-map $ϕ$ of the open unit disk $\mathbb{D}$ and its Koenigs eigenfunction. A generalization of orthogonality known as conjugate-orthogonality will play a key role in this work. We show that if $ϕ$ is a Schröder map (fixes a point $a\in \mathbb{D}$ with $0<|ϕ'(a)|<1$) and $σ$ is its Koenigs eigenfunction, then $C_ϕ$ is complex symmetric if and only if $(σ^n)_{n\in \mathbb{N}}$ is complete and conjugate-orthogonal in $H^2(\mathbb{D})$. We study the conjugate-orthogonality of Koenigs sequences with some concrete examples. We use these results to show that commutants of complex symmetric composition operators with Schröder symbols consist entirely of complex symmetric operators.
In this article, we study the complex symmetry of compositions operators $C_ϕf=f\circ ϕ$ induced on weighted Bergman spaces $A^2_β(\mathbb{D}),\ β\geq -1,$ by analytic self-maps of the unit disk. One of ours main results shows that $ϕ$ has a fixed point in $\mathbb{D}$ whenever $C_ϕ$ is complex symmetric. Our works establishes a strong relation between complex symmetry and cyclicity. By assuming $β\in \mathbb{N}$ and $ϕ$ is an elliptic automorphism of $\mathbb{D}$ which not a rotation, we show that $C_ϕ$ is not complex symmetric whenever $ϕ$ has order greater than $2(3+β).$
In this article, we completely characterize the complex symmetry, cyclicity and hypercyclicity of composition operators $C_ϕf=f\circϕ$ induced by affine self-maps $ϕ$ of the right half-plane $\mathbb{C}_+$ on the Hardy-Hilbert space $H^2(\mathbb{C}_+)$. We also provide new proofs for the normal, self-adjoint and unitary cases and for an adjoint formula discovered by Gallardo-Gutiérrez and Montes-Rodrígues.