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arXiv · 1706.04833

Eigenfunctions of Composition Operators on Bloch-type Spaces

Bhupendra Paudyal
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Abstract

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.

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Bhupendra Paudyal. 2017-06-15. Eigenfunctions of Composition Operators on Bloch-type Spaces. https://arxiv.org/abs/1706.04833

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