Bidiagonal factorization of tetradiagonal matrices and Darboux transformations
Recently a spectral Favard theorem for bounded banded lower Hessenberg matrices that admit a positive bidiagonal factorization was presented. These type of matrices are oscillatory. In this paper the Lima-Loureiro hypergeometric multiple orthogonal polynomials and the Jacobi-Pineiro multiple orthogo...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/72313 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/72313 |
| Access Level: | acceso abierto |
| Palabra clave: | 51-73 Tetradiagonal Hessenberg matrices Oscillatory matrices Totally nonnegative matrices Multiple orthogonal polynomials Favard spectral representation Darboux transformations Christoffel formulas Física-Modelos matemáticos Física matemática |
| Sumario: | Recently a spectral Favard theorem for bounded banded lower Hessenberg matrices that admit a positive bidiagonal factorization was presented. These type of matrices are oscillatory. In this paper the Lima-Loureiro hypergeometric multiple orthogonal polynomials and the Jacobi-Pineiro multiple orthogonal polynomials are discussed at the light of this bidiagonal factorization for tetradiagonal matrices. The Darboux transformations of tetradiagonal Hessenberg matrices is studied and Christoffel formulas for the elements of the bidiagonal factorization are given, i.e., the bidiagonal factorization is given in terms of the recursion polynomials evaluated at the origin. |
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