Non Abelian Toda-type equations and matrix valued orthogonal polynomials
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866914716297723904 |
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| author | Deaño, Alfredo Morey, Lucía Román, Pablo |
| author_facet | Deaño, Alfredo Morey, Lucía Román, Pablo |
| contents | In this paper, we study parameter deformations of matrix valued orthogonal polynomials (MVOPs). These deformations are built on the use of certain matrix valued operators which are symmetric with respect to the matrix valued inner product defined by the orthogonality weight. We show that the recurrence coefficients associated with these operators satisfy generalizations of the non-Abelian lattice equations. We provide a Lax pair formulation for these equations, and an example of deformed Hermite-type matrix valued polynomials is discussed in detail. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_14789 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Non Abelian Toda-type equations and matrix valued orthogonal polynomials Deaño, Alfredo Morey, Lucía Román, Pablo Classical Analysis and ODEs 37K10, 33C47, 33C45 In this paper, we study parameter deformations of matrix valued orthogonal polynomials (MVOPs). These deformations are built on the use of certain matrix valued operators which are symmetric with respect to the matrix valued inner product defined by the orthogonality weight. We show that the recurrence coefficients associated with these operators satisfy generalizations of the non-Abelian lattice equations. We provide a Lax pair formulation for these equations, and an example of deformed Hermite-type matrix valued polynomials is discussed in detail. |
| title | Non Abelian Toda-type equations and matrix valued orthogonal polynomials |
| topic | Classical Analysis and ODEs 37K10, 33C47, 33C45 |
| url | https://arxiv.org/abs/2302.14789 |