Model spaces invariant under composition operators

Authors

P. Muthukumar, Indian Institute of Technology Kanpur
Jaydeb Sarkar, Indian Statistical Institute Bangalore

Article Type

Research Article

Publication Title

Canadian Mathematical Bulletin

Abstract

Given a holomorphic self-map φ of D (the open unit disc in C), the composition operator Cφ f = f o φ, f ∈ H2(D), defines a bounded linear operator on the Hardy space H2(D). The model spaces are the backward shift-invariant closed subspaces of H2(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.

First Page

204

Last Page

217

DOI

https://10.4153/S0008439522000236

Publication Date

3-25-2023

Comments

Open Access, Green

Recommended Citation

Muthukumar, P. and Sarkar, Jaydeb, "Model spaces invariant under composition operators" (2023). Journal Articles. 3802.
https://digitalcommons.isical.ac.in/journal-articles/3802