On numerical invariants for submodules $[(z-w)^2]$ in $H^2(\mathbb{D}^2)$
Functional Analysis
2026-04-27 v1
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 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.
Cite
@article{arxiv.2604.22289,
title = {On numerical invariants for submodules $[(z-w)^2]$ in $H^2(\mathbb{D}^2)$},
author = {Yin Liu and Yufeng Lu and Chao Zu},
journal= {arXiv preprint arXiv:2604.22289},
year = {2026}
}