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arXiv · 2512.17388

On the membership of two-variable Rational Inner Functions in spaces of Dirichlet-type

Athanasios Beslikas·Alan Sola
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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 further record some consequences and variants of our main result.

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Athanasios Beslikas, Alan Sola. 2025-12-19. On the membership of two-variable Rational Inner Functions in spaces of Dirichlet-type. https://arxiv.org/abs/2512.17388

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