On modules of the Hardy space of Hartogs triangle
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915432029487104 |
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| author | Chattopadhyay, Arup Giri, Saikat Jain, Shubham |
| author_facet | Chattopadhyay, Arup Giri, Saikat Jain, Shubham |
| contents | In this paper, we investigate the structure of doubly commuting submodules and quotient modules of the Hardy space $H^2(\triangle_H)$ over the Hartogs triangle. We establish a complete classification of doubly commuting submodules. In addition, we characterize all doubly commuting quotient modules of the form $(θ_1(z/w)θ_2(w)H^2(\triangle_H))^\perp$, where $θ_1$ and $θ_2$ are inner functions on the unit disc. This is achieved by introducing the concept of $φ$-doubly commuting quotient modules on the Hardy space $H^2(\mathbb D^2).$ We further explore the essential normality and doubly commutativity of quotient modules of the form $(pH^2(\triangle_H))^\perp$ under some mild assumptions on $p$, where $p$ is a polynomial in two variables. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_04437 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On modules of the Hardy space of Hartogs triangle Chattopadhyay, Arup Giri, Saikat Jain, Shubham Functional Analysis 32Q02, 32H10, 47A15, 47A20, 30H10 In this paper, we investigate the structure of doubly commuting submodules and quotient modules of the Hardy space $H^2(\triangle_H)$ over the Hartogs triangle. We establish a complete classification of doubly commuting submodules. In addition, we characterize all doubly commuting quotient modules of the form $(θ_1(z/w)θ_2(w)H^2(\triangle_H))^\perp$, where $θ_1$ and $θ_2$ are inner functions on the unit disc. This is achieved by introducing the concept of $φ$-doubly commuting quotient modules on the Hardy space $H^2(\mathbb D^2).$ We further explore the essential normality and doubly commutativity of quotient modules of the form $(pH^2(\triangle_H))^\perp$ under some mild assumptions on $p$, where $p$ is a polynomial in two variables. |
| title | On modules of the Hardy space of Hartogs triangle |
| topic | Functional Analysis 32Q02, 32H10, 47A15, 47A20, 30H10 |
| url | https://arxiv.org/abs/2508.04437 |