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arXiv · 2604.22289

On numerical invariants for submodules $[(z-w)^2]$ in $H^2(\mathbb{D}^2)$

Yin Liu·Yufeng Lu·Chao Zu
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Abstract

In this paper, we study numerical invariants associated with a homogeneous submodule of the Hardy module over the bidisk. We focus on the submodule generated by the polynomial $(z-w)^2$ and obtain explicit formulas for the corresponding invariants. As an application, we verify the monotonicity property in this concrete setting. Our results provide a detailed example illustrating the behavior of these invariants beyond the linear case.

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Yin Liu, Yufeng Lu, Chao Zu. 2026-04-24. On numerical invariants for submodules $[(z-w)^2]$ in $H^2(\mathbb{D}^2)$. https://doi.org/10.1007/s40840-026-02132-3

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