Model spaces invariant under composition operators

Muthukumar, P. ; Sarkar, Jaydeb 

Canadian mathematical bulletin, Tome 66 (2023) no. 1, pp. 204-217

Résumé

Given a holomorphic self-map $\varphi $ of $\mathbb {D}$ (the open unit disc in $\mathbb {C}$), the composition operator $C_{\varphi } f = f \circ \varphi $, $f \in H^2(\mathbb {\mathbb {D}})$, 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.

Détail

DOI : 10.4153/S0008439522000236

Mots-clés : Composition operators, inner functions, model spaces, Hardy space, fractional linear transformations, Blaschke products