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arXiv · 2608.29722

Singular inner eigenfunctions of composition operators

V. A. Anjali·P. Muthukumar·P. Shankar
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Abstract

This paper characterizes all the singular inner eigenfunctions of the composition operators $C_\phi$ that arise from discrete measures, when $\phi$ 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.

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V. A. Anjali, P. Muthukumar, P. Shankar. 2026-08-30. Singular inner eigenfunctions of composition operators. https://arxiv.org/abs/2608.29722

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