On the membership of two-variable rational inner functions in spaces of Dirichlet type
Studia Mathematica
MSC: Primary 32A08; Secondary 32A37, 46E22
DOI: 10.4064/sm260102-6-5
Published online: 3 November 2026
Abstract
We study membership of rational inner functions on the bidisk $\mathbb {D}^2$ 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 record some consequences and variants of our main result.
