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arXiv · 2603.10575

Shadowing phenomenon for composition operators on the Hardy space $H^2(\mathbb{D})$

Artur Blois·Ben-Hur Eidt·Paulo Lupatini·Osmar R. Severiano
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Abstract

Let $\phi$ be a holomorphic self-map of the open unit disk $\mathbb{D}.$ In this article, we study the shadowing phenomenon for composition operators $C_{\phi}f=f\circ \phi$ 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.

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Artur Blois, Ben-Hur Eidt, Paulo Lupatini, Osmar R. Severiano. 2026-03-11. Shadowing phenomenon for composition operators on the Hardy space $H^2(\mathbb{D})$. https://arxiv.org/abs/2603.10575

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