On the membership of two-variable Rational Inner Functions in spaces of Dirichlet-type
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917412554670080 |
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| author | Beslikas, Athanasios Sola, Alan |
| author_facet | Beslikas, Athanasios Sola, Alan |
| contents | We study membership of rational inner functions on the bidisk $\mathbb{D}^2$ in a scale of Dirichlet spaces considered by Bera, Chavan, and Ghara, and in higher-order variants of these spaces. We give a characterization for membership in terms of the geometric concept of contact order of a rational inner function at its singular points, and we further record some consequences and variants of our main result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_17388 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the membership of two-variable Rational Inner Functions in spaces of Dirichlet-type Beslikas, Athanasios Sola, Alan Complex Variables 32A08, 32A37, 46E22 We study membership of rational inner functions on the bidisk $\mathbb{D}^2$ in a scale of Dirichlet spaces considered by Bera, Chavan, and Ghara, and in higher-order variants of these spaces. We give a characterization for membership in terms of the geometric concept of contact order of a rational inner function at its singular points, and we further record some consequences and variants of our main result. |
| title | On the membership of two-variable Rational Inner Functions in spaces of Dirichlet-type |
| topic | Complex Variables 32A08, 32A37, 46E22 |
| url | https://arxiv.org/abs/2512.17388 |