On numerical invariants for submodules $[(z-w)^2]$ in $H^2(\mathbb{D}^2)$
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866913058980364288 |
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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 |
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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 |