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

Abstract

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

15 pages