Properties of Matrix Orthogonal Polynomials via their Riemann-Hilbert Characterization
We give a Riemann–Hilbert approach to the theory of matrix orthogonal polynomials. We will focus on the algebraic aspects of the problem, obtaining difference and differential relations satisfied by the corresponding orthogonal polynomials. We will show that in the matrix case there is some extra fr...
| Main Authors: | , , |
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| Format: | info:eu-repo/semantics/article |
| Language: | English |
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2012
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| Subjects: | |
| Online Access: | http://hdl.handle.net/10835/1591 |
| _version_ | 1789406428267544576 |
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| author | Grünbaum, F. Alberto De la Iglesia, Manuel D. Martínez-Finkelshtein, Andrei |
| author_facet | Grünbaum, F. Alberto De la Iglesia, Manuel D. Martínez-Finkelshtein, Andrei |
| author_sort | Grünbaum, F. Alberto |
| collection | DSpace |
| description | We give a Riemann–Hilbert approach to the theory of matrix orthogonal polynomials. We will focus on the algebraic aspects of the problem, obtaining difference and differential relations satisfied by the corresponding orthogonal polynomials. We will show that in the matrix case there is some extra freedom that allows us to obtain a family of ladder operators, some of them of 0-th order, something that is not possible in the scalar case. The combination of the ladder operators will lead to a family of second-order differential equations satisfied by the orthogonal polynomials, some of them of 0-th and first order, something also impossible in the scalar setting. This shows that the differential properties in the matrix case are much more complicated than in the scalar situation. We will study several examples given in the last years as well as others not considered so far. |
| format | info:eu-repo/semantics/article |
| id | oai:repositorio.ual.es:10835-1591 |
| institution | Universidad de Cuenca |
| language | English |
| publishDate | 2012 |
| record_format | dspace |
| spelling | oai:repositorio.ual.es:10835-15912023-04-12T19:37:21Z Properties of Matrix Orthogonal Polynomials via their Riemann-Hilbert Characterization Grünbaum, F. Alberto De la Iglesia, Manuel D. Martínez-Finkelshtein, Andrei Matriz de polinomios ortogonales Matrix orthogonal polynomials Riemann–Hilbert We give a Riemann–Hilbert approach to the theory of matrix orthogonal polynomials. We will focus on the algebraic aspects of the problem, obtaining difference and differential relations satisfied by the corresponding orthogonal polynomials. We will show that in the matrix case there is some extra freedom that allows us to obtain a family of ladder operators, some of them of 0-th order, something that is not possible in the scalar case. The combination of the ladder operators will lead to a family of second-order differential equations satisfied by the orthogonal polynomials, some of them of 0-th and first order, something also impossible in the scalar setting. This shows that the differential properties in the matrix case are much more complicated than in the scalar situation. We will study several examples given in the last years as well as others not considered so far. 2012-07-12T11:52:52Z 2012-07-12T11:52:52Z 2011 info:eu-repo/semantics/article 1815-0659 http://hdl.handle.net/10835/1591 en info:eu-repo/semantics/openAccess SIGMA Volumen 7 (2011), 098 |
| spellingShingle | Matriz de polinomios ortogonales Matrix orthogonal polynomials Riemann–Hilbert Grünbaum, F. Alberto De la Iglesia, Manuel D. Martínez-Finkelshtein, Andrei Properties of Matrix Orthogonal Polynomials via their Riemann-Hilbert Characterization |
| title | Properties of Matrix Orthogonal Polynomials via their Riemann-Hilbert Characterization |
| title_full | Properties of Matrix Orthogonal Polynomials via their Riemann-Hilbert Characterization |
| title_fullStr | Properties of Matrix Orthogonal Polynomials via their Riemann-Hilbert Characterization |
| title_full_unstemmed | Properties of Matrix Orthogonal Polynomials via their Riemann-Hilbert Characterization |
| title_short | Properties of Matrix Orthogonal Polynomials via their Riemann-Hilbert Characterization |
| title_sort | properties of matrix orthogonal polynomials via their riemann-hilbert characterization |
| topic | Matriz de polinomios ortogonales Matrix orthogonal polynomials Riemann–Hilbert |
| url | http://hdl.handle.net/10835/1591 |
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