Model spaces invariant under composition operators. Issue 1 (25th March 2023) - Muthukumar, P.; Sarkar, Jaydeb
Abstract: Given a holomorphic self-map $φ $ of $\mathbb {D}$ (the open unit disc in $\mathbb {C}$ ), the composition operator $C_{φ } f = f ° φ $, $f \in H^2(\mathbb {\mathbb {D}})$, defines a bounded linear operator on the Hardy space $H^2(\mathbb {\mathbb {D}})$ . The model spaces are the backward shift-invariant closed subspaces of $H^2(\mathbb {\mathbb {D}})$, which are canonically associated with inner functions. In this paper, we study model spaces that are invariant under composition operators. Emphasis is put on finite-dimensional model spaces, affine transformations, and linear fractional transformations.