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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.17694 |
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| _version_ | 1866908683145838592 |
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| author | Mañas, Manuel Rojas, Miguel Wu, Jianwen |
| author_facet | Mañas, Manuel Rojas, Miguel Wu, Jianwen |
| contents | This article studies bivariate multiple orthogonal polynomials of the mixed type on the step-line. The analysis is based on the LU factorization of a moment matrix specifically adapted to this framework. The orthogonality and biorthogonality relations satisfied by these polynomials are identified, and their precise multi-degrees are determined. The corresponding recurrence relations and the growing band matrices that encode them are also derived. Christoffel-Darboux kernels and the associated Christoffel-Darboux-type formulas are obtained. An ABC-type theorem is established, relating the inverse of the truncated moment matrix to these kernels. As an illustration, the bivariate Jacobi-Piñeiro multiple orthogonal polynomials of mixed type on the triangle are computed by means of an LU factorization implemented in a dedicated Maple script. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_17694 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bivariate multiple orthogonal polynomials of mixed type on the step-line Mañas, Manuel Rojas, Miguel Wu, Jianwen Classical Analysis and ODEs Mathematical Physics 42C05, 33BXX This article studies bivariate multiple orthogonal polynomials of the mixed type on the step-line. The analysis is based on the LU factorization of a moment matrix specifically adapted to this framework. The orthogonality and biorthogonality relations satisfied by these polynomials are identified, and their precise multi-degrees are determined. The corresponding recurrence relations and the growing band matrices that encode them are also derived. Christoffel-Darboux kernels and the associated Christoffel-Darboux-type formulas are obtained. An ABC-type theorem is established, relating the inverse of the truncated moment matrix to these kernels. As an illustration, the bivariate Jacobi-Piñeiro multiple orthogonal polynomials of mixed type on the triangle are computed by means of an LU factorization implemented in a dedicated Maple script. |
| title | Bivariate multiple orthogonal polynomials of mixed type on the step-line |
| topic | Classical Analysis and ODEs Mathematical Physics 42C05, 33BXX |
| url | https://arxiv.org/abs/2507.17694 |