On the Christoffel–Darboux formula for generalized matrix orthogonal polynomials
| dc.contributor.author | Álvarez Fernández, Carlos | |
| dc.contributor.author | Mañas Baena, Manuel Enrique | |
| dc.date.accessioned | 2023-06-19T14:54:46Z | |
| dc.date.available | 2023-06-19T14:54:46Z | |
| dc.date.issued | 2014-10-01 | |
| dc.description | ©2014 Elsevier Inc. All rights reserved. MM thanks economical support from the Spanish “Ministerio de Economía y Competitividad” research project MTM2012-36732-C03-01, Ortogonalidad y aproximacion; Teoria y Aplicaciones. | |
| dc.description.abstract | We obtain an extension of the Christoffel–Darboux formula for matrix orthogonal polynomials with a generalized Hankel symmetry, including the Adler-van Moerbeke generalized orthogonal polynomials | |
| dc.description.department | Depto. de Física Teórica | |
| dc.description.faculty | Fac. de Ciencias Físicas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Ministerio de Economía y Competitividad (MINECO) | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/30968 | |
| dc.identifier.doi | 10.1016/j.jmaa.2014.03.094 | |
| dc.identifier.issn | 0022-247X | |
| dc.identifier.officialurl | http://dx.doi.org/10.1016/j.jmaa.2014.03.094 | |
| dc.identifier.relatedurl | http://www.sciencedirect.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/34736 | |
| dc.issue.number | 1 | |
| dc.journal.title | Journal of mathematical analysis and applications | |
| dc.language.iso | eng | |
| dc.page.final | 247 | |
| dc.page.initial | 238 | |
| dc.publisher | Elsevier | |
| dc.relation.projectID | MTM2012-36732-C03-01 | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 51-73 | |
| dc.subject.keyword | Generalized matrix orthogonal polynomials | |
| dc.subject.keyword | Christoffel–Darboux formula | |
| dc.subject.keyword | multigradedHankel symmetry. | |
| dc.subject.ucm | Física-Modelos matemáticos | |
| dc.subject.ucm | Física matemática | |
| dc.title | On the Christoffel–Darboux formula for generalized matrix orthogonal polynomials | |
| dc.type | journal article | |
| dc.volume.number | 418 | |
| dcterms.references | [1] M. Adler and P. van Moerbeke, Group factorization, moment matrices and Toda lattices, International Mathe- matical Research Notices 12 (1997) 556-572. [2] M. Adler and P. van Moerbeke, Generalized orthogonal polynomials, discrete KP and Riemann–Hilbert problems, Communications in Mathematical Physics 207 (1999) 589-620. [3] M. Adler and P. van Moerbeke, Darboux transforms on band matrices, weights and associated polynomials, Inter- national Mathematical Research Notices 18 (2001) 935-984. [4] M. Adler, P. van Moerbeke, and P. Vanhaecke, Moment matrices and multi-component KP, with applications to random matrix theory, Communications in Mathematical Physics 286 (2009) 1-38. [5] C. Alvarez-Fern ánndez, U. Fidalgo, and M. Mañas, The multicomponent 2D Toda hierarchy: generalized matrix orthogonal polynomials, multiple orthogonal polynomials and Riemann–Hilbert problems, Inverse Problems 26 (2010) 055009 (17 pp.) [6] C. Álvarez-Fern ández, U. Fidalgo, and M. Mañas, Multiple orthogonal polynomials of mixed type: Gauss-Borel factorization and the multi-component 2D Toda hierarchy, Advances in Mathematics 227 (2011) 1451-1525. [7] C. Alvarez-Fernández and M.Mañas, Orthogonal Laurent polynomials on the unit circle, extended CMV ordering and 2D Toda type integrable hierarchies, Advances in Mathematics 240 (2013) 132193. [8] M. J. Bergvelt and A. P. E. ten Kroode, Partitions, vertex operators constructions and multi- component KP equations, Pacific Journal of Mathematics 171 (1995) 23-88. [9] M. Cafasso, Matrix Biorthogonal Polynomials on the unit circle and the non-Abelian Ablowitz-Ladik hierarchy, Jounal of Physics A: Mathematical and Theoritical 42 (2009), 365211. [10] R. Cruz-Barroso and P. Gonz ález-Vera, A Christoffel–Darboux formula and a Favard’s theorem for Laurent or- thogonal polynomials on the unit circle, Journal of Computational and Applied Mathematics 179 (2005) ,157-173. [11] E. Daems and A. B. J. Kuijlaars, A Christoffel–Darboux formula for multiple orthogonal polynomials, Journal of Approximation Theory 130 (2004) 188-200. [12] E. Daems and A. B. J. Kuijlaars, Multiple orthogonal polynomials of mixed type and non- intersecting Brownian motions, Journal of Approximation Theory 146 (2007) 91-114. [13] A. S. Fokas, A. R. Its, and A. V. Kitaev, The isomonodromy approach to matrix models in 2D quatum gravity, Communications in Mathematical Physics (1992) 395-430. [14] M. Mañas, L. Martínez Alonso, and C. Alvarez-Fernandez, The multicomponent 2D Toda hierarchy: discrete flows and string equations, Inverse Problems 25 (2009) 065007 (31 pp). [15] M. Mañas and L. Martínez Alonso, The multicomponent 2D Toda hierarchy: dispersionless limit, Inverse Problems 25 (2009) 115020 (22 pp). [16] M. Mulase, Complete integrability of the Kadomtsev–Petviashvili equation, Advances in Mathematics 54 (1984) 57-66. [17] M. Sato, Soliton equations as dynamical systems on infinite dimensional Grassmann manifolds, Research Institute for Mathematical Sciences Kokyuroku 439 (1981) 30-46. [18] B. Simon, The Christoffel–Darboux Kernel, Proceedings of Symposia in Pure Mathematics 79:“Perspectives in Partial Differential Equations, Harmonic Analysis and Applications: A Volume in Honor of Vladimir G. Maz’ya’s 70th Birthday”, (2008) 295-336. arXiv:0806.1528 [19] K. Ueno and K. Takasaki, Toda lattice hierarchy, in Group Representations and Systems of Differential Equations, Advanced Studies in Pure Mathematics 4 (1984) 1-95. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 0d5b5872-7553-4b33-b0e5-085ced5d8f42 | |
| relation.isAuthorOfPublication.latestForDiscovery | 0d5b5872-7553-4b33-b0e5-085ced5d8f42 |
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