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# The multicomponent 2D Toda hierarchy: generalized matrix orthogonal polynomials, multiple orthogonal polynomials and Riemann-Hilbert problems

Inverse Problems (Impact Factor: 1.8). 05/2010; 26(5). DOI: 10.1088/0266-5611/26/5/055009
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ABSTRACT 15 pages.-- ArXiv pre-print available at: http://arxiv.org/abs/0911.0941 Submitted to: Inverse Problems We consider the relation of the multi-component 2D Toda hierarchy with matrix orthogonal and biorthogonal polynomials. The multi-graded Hankel reduction of this hierarchy is considered and the corresponding generalized matrix orthogonal polynomials are studied. In particular for these polynomials we consider the recursion relations, and for rank one weights its relation with multiple orthogonal polynomials of mixed type with a type II normalization and the corresponding link with a Riemann--Hilbert problem. MM thanks economical support from the Spanish Ministerio de Ciencia e Innovación, research project FIS2008-00200 and UF thanks economical support from the Spanish Ministerio de Ciencia e Innovación research projects MTM2006-13000-C03-02 and MTM2007-62945 and from Comunidad de Madrid/Universidad Carlos III de Madrid project CCG07-UC3M/ESP-3339. No publicado

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