Work

Singular inner eigenfunctions of composition operators

Year: 2026

Type: preprint

Abstract: This paper characterizes all the singular inner eigenfunctions of the composition operators $C_ϕ$ that arise from discrete measures, when $ϕ$ is an automorphism of unit disk. By establishing a connection between Beurling and model invariant subspaces, we classify all the inner functions so that the corresponding Beurling subspace is invariant under the composition operators induced by non-elliptic automorphisms. This classification involves solving the eigenfunction equation for the composition operator. Further, we present some applications of the above-mentioned connection.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2608.29722

Authors: Anjali, V. A., Muthukumar, P., Shankar, P.

Language: English

Topic: Holomorphic and Operator Theory

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Department of Science and Technology, Ministry of Science and Technology, India

OpenAlex ID: W7204942047

Cites: 1

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Related to: 10