General Geronimus Perturbations for Mixed Multiple Orthogonal Polynomials
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915032820875264 |
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| author | Mañas, Manuel Rojas, Miguel |
| author_facet | Mañas, Manuel Rojas, Miguel |
| contents | General Geronimus transformations, defined by regular matrix polynomials that are neither required to be monic nor restricted by the rank of their leading coefficients, are applied through both right and left multiplication to a rectangular matrix of measures associated with mixed multiple orthogonal polynomials. These transformations produce Christoffel-type formulas that establish relationships between the perturbed and original polynomials. Moreover, it is proven that the existence of Geronimus-perturbed orthogonality is equivalent to the non-cancellation of certain $τ$-determinants. The effect of these transformations on the Markov-Stieltjes matrix functions is also determined. As a case study, we examine the Jacobi-Piñeiro orthogonal polynomials with three weights. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_16022 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | General Geronimus Perturbations for Mixed Multiple Orthogonal Polynomials Mañas, Manuel Rojas, Miguel Classical Analysis and ODEs Mathematical Physics 42C05, 33C45, 33C47, 47B39, 47B36 General Geronimus transformations, defined by regular matrix polynomials that are neither required to be monic nor restricted by the rank of their leading coefficients, are applied through both right and left multiplication to a rectangular matrix of measures associated with mixed multiple orthogonal polynomials. These transformations produce Christoffel-type formulas that establish relationships between the perturbed and original polynomials. Moreover, it is proven that the existence of Geronimus-perturbed orthogonality is equivalent to the non-cancellation of certain $τ$-determinants. The effect of these transformations on the Markov-Stieltjes matrix functions is also determined. As a case study, we examine the Jacobi-Piñeiro orthogonal polynomials with three weights. |
| title | General Geronimus Perturbations for Mixed Multiple Orthogonal Polynomials |
| topic | Classical Analysis and ODEs Mathematical Physics 42C05, 33C45, 33C47, 47B39, 47B36 |
| url | https://arxiv.org/abs/2411.16022 |