On the membership of two-variable Rational Inner Functions in spaces of Dirichlet-type
Abstract
We study membership of rational inner functions on the bidisk in a scale of Dirichlet spaces considered by Bera, Chavan, and Ghara, and in higher-order variants of these spaces. We give a characterization for membership in terms of the geometric concept of contact order of a rational inner function at its singular points, and we further record some consequences and variants of our main result.
Cite
@article{arxiv.2512.17388,
title = {On the membership of two-variable Rational Inner Functions in spaces of Dirichlet-type},
author = {Athanasios Beslikas and Alan Sola},
journal= {arXiv preprint arXiv:2512.17388},
year = {2026}
}
Comments
Accepted for publication in Studia Mathematica. In the published version of the article, we provided a more brief proof by using only one Blaschke factor per referee's request. In this version we still apply Referee's lemma and we keep the original proof, in order to showcase the usefullness of local factorizations in the RIF theory. Our main result now is a full characterization