The Toda and Painlevé Systems Associated with Semiclassical Matrix-Valued Orthogonal Polynomials of Laguerre Type
Consider the Laguerre polynomials and deform them by the introduction in the measure of an exponential singularity at zero. In [Chen Y., Its A., J. Approx. Theory 162 (2010), 270-297], the authors proved that this deformation can be described by systems of differential/difference equations for the c...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2018 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2018
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/209774 |
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| Cite this: | The Toda and Painlevé Systems Associated with Semiclassical Matrix-Valued Orthogonal Polynomials of Laguerre Type / M. Cafasso, M.D. de la Iglesia // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 19 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862671905051377664 |
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| author | Cafasso, M., de la Iglesia, M.D. |
| author_facet | Cafasso, M., de la Iglesia, M.D. |
| citation_txt | The Toda and Painlevé Systems Associated with Semiclassical Matrix-Valued Orthogonal Polynomials of Laguerre Type / M. Cafasso, M.D. de la Iglesia // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 19 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Consider the Laguerre polynomials and deform them by the introduction in the measure of an exponential singularity at zero. In [Chen Y., Its A., J. Approx. Theory 162 (2010), 270-297], the authors proved that this deformation can be described by systems of differential/difference equations for the corresponding recursion coefficients and that these equations, ultimately, are equivalent to the Painlevé III equation and its Bäcklund/Schlesinger transformations. Here, we prove that an analogue result holds for some kind of semiclassical matrix-valued orthogonal polynomials of Laguerre type.
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| first_indexed | 2025-12-07T15:34:47Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-209774 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T15:34:47Z |
| publishDate | 2018 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Cafasso, M., de la Iglesia, M.D. 2025-11-26T11:34:49Z 2018 The Toda and Painlevé Systems Associated with Semiclassical Matrix-Valued Orthogonal Polynomials of Laguerre Type / M. Cafasso, M.D. de la Iglesia // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 19 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 34M56; 35Q15; 37J35; 42C05 arXiv: 1801.08740 https://nasplib.isofts.kiev.ua/handle/123456789/209774 https://doi.org/10.3842/SIGMA.2018.076 Consider the Laguerre polynomials and deform them by the introduction in the measure of an exponential singularity at zero. In [Chen Y., Its A., J. Approx. Theory 162 (2010), 270-297], the authors proved that this deformation can be described by systems of differential/difference equations for the corresponding recursion coefficients and that these equations, ultimately, are equivalent to the Painlevé III equation and its Bäcklund/Schlesinger transformations. Here, we prove that an analogue result holds for some kind of semiclassical matrix-valued orthogonal polynomials of Laguerre type. M.C. acknowledges the financial support of the Universidad Nacional Autónoma de México (UNAM) and the Unité Mixte International (UMI) “Laboratoire Solomon Lefschetz”, and thanks their staff for the hospitality during his stay in Mexico. We both acknowledge the financial support of the Instituto de Ciencias Matemáticas (ICMAT) for our stay in Madrid during the thematic program “Orthogonal polynomials and special functions in Mathematical Physics and Approximation Theory”, and we are particularly grateful to David Gómez-Ullate for his invitation to participate. Finally, the work of the first author is also supported by the project IPaDEGAN (H2020-MSCA-RISE-2017), grant number 778010 (European Union), and the work of the second one by PAPIIT-DGAPA-UNAM grant IA102617 (Mexico). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Toda and Painlevé Systems Associated with Semiclassical Matrix-Valued Orthogonal Polynomials of Laguerre Type Article published earlier |
| spellingShingle | The Toda and Painlevé Systems Associated with Semiclassical Matrix-Valued Orthogonal Polynomials of Laguerre Type Cafasso, M., de la Iglesia, M.D. |
| title | The Toda and Painlevé Systems Associated with Semiclassical Matrix-Valued Orthogonal Polynomials of Laguerre Type |
| title_full | The Toda and Painlevé Systems Associated with Semiclassical Matrix-Valued Orthogonal Polynomials of Laguerre Type |
| title_fullStr | The Toda and Painlevé Systems Associated with Semiclassical Matrix-Valued Orthogonal Polynomials of Laguerre Type |
| title_full_unstemmed | The Toda and Painlevé Systems Associated with Semiclassical Matrix-Valued Orthogonal Polynomials of Laguerre Type |
| title_short | The Toda and Painlevé Systems Associated with Semiclassical Matrix-Valued Orthogonal Polynomials of Laguerre Type |
| title_sort | toda and painlevé systems associated with semiclassical matrix-valued orthogonal polynomials of laguerre type |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/209774 |
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