## Eigenfunctions of Composition Operators on Bloch-type Spaces. (arXiv:1706.04833v2 [math.CV] UPDATED)

Suppose $\varphi$ is a holomorphic self map of the unit disk and $C_\varphi$ is a composition operator with symbol $\varphi$ that fixes the origin and $0&lt;|\varphi'(0)|&lt;1$. This work explores sufficient conditions that ensure all holomorphic solutions of Schr\"oder equation for the composition operator $C_\varphi$ belong to a Bloch-type space $\mathcal{B}_\alpha$ for some $\alpha&gt;0$. The results from composition operators have been extended to weighted composition operators in the second part of this work.查看全文

## Solidot 文章翻译

 你的名字 留空匿名提交 你的Email或网站 用户可以联系你 标题 简单描述 内容 Suppose $\varphi$ is a holomorphic self map of the unit disk and $C_\varphi$ is a composition operator with symbol $\varphi$ that fixes the origin and $0<|\varphi'(0)|<1$. This work explores sufficient conditions that ensure all holomorphic solutions of Schr\"oder equation for the composition operator $C_\varphi$ belong to a Bloch-type space $\mathcal{B}_\alpha$ for some $\alpha>0$. The results from composition operators have been extended to weighted composition operators in the second part of this work.