General geronimus perturbations for mixed multiple orthogonal polynomials
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 orthogona...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/124486 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/124486 |
| Access Level: | acceso abierto |
| Palabra clave: | 51-73 Mixed multiple orthogonal polynomials Geronimus perturbations Christoffel formulas Spectral theory of matrix polynomials Física matemática 2212 Física Teórica |
| Sumario: | 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. |
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