Properties of Matrix Orthogonal Polynomials via their Riemann-Hilbert Characterization
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Properties of Matrix Orthogonal Polynomials via their Riemann-Hilbert Characterization
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| Creator |
Grünbaum, F.A.
de la Iglesia, M.D. Martínez-Finkelshtein, A. |
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| 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.
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| Date |
2019-02-15T17:09:49Z
2019-02-15T17:09:49Z 2011 |
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| Type |
Article
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| Identifier |
Properties of Matrix Orthogonal Polynomials via their Riemann-Hilbert Characterization / F.A. Grünbaum, M.D. de la Iglesia, A. Martínez-Finkelshtein // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 52 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 42C05; 35Q15 http://dspace.nbuv.gov.ua/handle/123456789/147659 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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