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

Fuente: arXiv
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Main Authors: Liu, Yin, Lu, Yufeng, Zu, Chao
Format: Preprint
Published: 2026
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author Liu, Yin
Lu, Yufeng
Zu, Chao
author_facet Liu, Yin
Lu, Yufeng
Zu, Chao
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2604_22289
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle On numerical invariants for submodules $[(z-w)^2]$ in $H^2(\mathbb{D}^2)$
Liu, Yin
Lu, Yufeng
Zu, Chao
Functional Analysis
Primary 46E22 Secondary 47A13
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.
title On numerical invariants for submodules $[(z-w)^2]$ in $H^2(\mathbb{D}^2)$
topic Functional Analysis
Primary 46E22 Secondary 47A13
url https://arxiv.org/abs/2604.22289