Let $H^2$ denote the Hardy space on the open unit disk $\mathbb{D}$. For a given holomorphic self map $\varphi$ of $\mathbb{D}$, the composition operator $C_\varphi$ on $H^2$ is defined by $C_\varphi(f) = f \circ \varphi$. In this talk, we discuss about Beurling type invariant subspace of composition operators, that is common invariant subspaces of shift (multiplication) and composition operators. We will also consider the model spaces that are invariant under composition operators.

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Last updated: 08 Jun 2023