English

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 (zw)2(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.

Keywords

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}
}
R2 v1 2026-07-01T12:33:27.361Z