双变量有理内函数在 Dirichlet 空间中的成员资格问题
复变函数
2026-04-17 v2
摘要
我们研究了双变量有理内函数在 Bera、Chavan 与 Ghara 所考察的 Dirichlet 空间序列以及这些空间的更高阶变体中的成员资格问题。我们给出了关于有理内函数在其奇点处接触阶数的几何概念的成员资格判别，并进一步记录了我们的主要结果的若干推论与变体。
关键词
引用
@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}
}
备注
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