Approximation and orthogonality on fully symmetric domains
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909784119181312 |
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| author | Xu, Yuan |
| author_facet | Xu, Yuan |
| contents | We study orthogonal polynomials on a fully symmetric planar domain $Ω$ that is generated by a certain triangle in the first quadrant. For a family of weight functions on $Ω$, we show that orthogonal polynomials that are even in the second variable on $Ω$ can be identified with orthogonal polynomials on the unit disk composed with a quadratic map, and the same phenomenon can be extended to the domain generated by the rotation of $Ω$ in higher dimensions. The connection allows an immediate deduction of results for approximation and Fourier orthogonal expansions on these fully symmetric domains. It applies, for example, to analysis on a double cone or a double hyperboloid. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_10342 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Approximation and orthogonality on fully symmetric domains Xu, Yuan Classical Analysis and ODEs 33C45, 42C05, 42C10 We study orthogonal polynomials on a fully symmetric planar domain $Ω$ that is generated by a certain triangle in the first quadrant. For a family of weight functions on $Ω$, we show that orthogonal polynomials that are even in the second variable on $Ω$ can be identified with orthogonal polynomials on the unit disk composed with a quadratic map, and the same phenomenon can be extended to the domain generated by the rotation of $Ω$ in higher dimensions. The connection allows an immediate deduction of results for approximation and Fourier orthogonal expansions on these fully symmetric domains. It applies, for example, to analysis on a double cone or a double hyperboloid. |
| title | Approximation and orthogonality on fully symmetric domains |
| topic | Classical Analysis and ODEs 33C45, 42C05, 42C10 |
| url | https://arxiv.org/abs/2509.10342 |