论文标题
复杂的对称性和koenigs本征函数之间的相互作用
Interplay between complex symmetry and Koenigs eigenfunctions
论文作者
论文摘要
我们研究了由开放单位磁盘的分析自动映射$ ϕ $及其koenigs eigenigs eigenigs eigenfunuttion。被称为共轭 - 实行性的正交性的概括将在这项工作中起关键作用。我们表明，如果$ ϕ $是schröder地图（用$ 0 <| 0 <| ϕ'（a）| <1 $）和$σ$是其koenigs egenigs eigenfunction，那么$ c_x $是$ c_D $，那么$ c_D $ ar是复杂的IF（IS），iS ig（n） $ h^2（\ mathbb {d}）$中的共轭 - 正交。我们研究了Koenigs序列的共轭 - 正交性，其中一些具体的例子。我们使用这些结果表明，具有Schröder符号的复杂对称成分运算符的通勤者完全由复杂的对称操作员组成。
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.
