PreprintCC BY 4.0arXiv
Singular inner eigenfunctions of composition operators
Abstract
This paper characterizes all the singular inner eigenfunctions of the composition operators Cϕ 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.
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BibTeX
@misc{anjali2026singular,
title = {{Singular inner eigenfunctions of composition operators}},
author = {V. A. Anjali and P. Muthukumar and P. Shankar},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29722},
eprint = {2608.29722},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29722},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Singular inner eigenfunctions of composition operators
AU - V. A. Anjali
AU - P. Muthukumar
AU - P. Shankar
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2608.29722
UR - https://arxiv.org/abs/2608.29722
AB - 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.
ER -