RT Journal Article
T1 The multicomponent 2D Toda hierarchy: generalized matrix orthogonal polynomials, multiple orthogonal polynomials and Riemann-Hilbert problems
A1 Álvarez Fernández, Carlos
A1 Fidalgo Prieto, Ulises
A1 Mañas Baena, Manuel
AB We consider the relation of the multicomponent 2D Toda hierarchy with the 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 1 weights its relation with multiple orthogonal polynomials of mixed type with a type II normalization and the corresponding link with a Riemann-Hilbert problem.
PB IOP Publishing
SN 0266-5611
YR 2010
FD 2010-05
LK https://hdl.handle.net/20.500.14352/44699
UL https://hdl.handle.net/20.500.14352/44699
LA eng
NO [1] E. Daems and A. B. J. Kuijlaars, J. of Approx. Theory 146 (2007) 91. [2] A. Durán and F. A. Grünbaum, J. Compt. Appl. Math. 178 (2005) 169. [3] M. Adler, P. van Moerbeke and P. Vanhaecke, Commun. Math. Phys. 286 (2008) 1. [4] L. Martínez Alonso and E. Medina, J. Phys. A: Math. Theor. 42 (2009) 205204. [5] M. Adler and P. van Moerbeke, Commun. Math. Phys. 207 (1999) 589. [6] M. Adler and P. van Moerbeke, Int. Math. Res. Not. 18 (2001) 935. [7] M. Cafasso, J. Phys. A: Math. Theor. 42 (2009) 365211. [8] K. Ueno and K. Takasaki, Adv. Stud. Pure Math. 4 (1984) 1. [9] M. Mulase, Adv. Math. 54 (1984) 57. [10] M. Mañas, L. Martínez Alonso and C. Alvarez- Fernández, Inv. Prob. 25 (2009) 065007. [11] M. Mañas and L. Martínez Alonso, Inv. Prob. To be appear (2009). [12] R. Felipe and F. Ongay, Lin. Alg. Appl. 338 (2001) 1. [13] W. Van Assche, K. T-R Mc Laughlin, A. B. J. Kuijlaars and M. Vanlessen, Adv. Math. 188 (2004) 337. [14] F.D. Gakhov. Boundary Value Problems, Pergamon Press, New York, (1966). Redited by Dover (1990).
NO ©IOP Publishing.For financial support MM thanks the Spanish Ministerio de Ciencia e Innovacion, research project FIS2008-00200 and UF thanks the SFRH/BPD/62947/2009, Fundaçao para a Ciéncia e ˆa Tecnologia of Portugal, PT2009-0031, Acciones Integradas Portugal, Ministerio de Ciencia e Innovacion de España, and MTM2009-12740-C03-01. Ministerio de Ciencia e Innovación de Espana. MM acknowledges different clarifying discussions with Dr Mattia Caffasso, Prof. Pierre van Moerbeke, Prof Luis Mart´ınez Alonso and Prof David Gomez-Ullate.
NO Ministerio de Ciencia e Innovacion, Spain
NO Fundacao para a Ciencia e a Tecnologia of Portugal
NO Acciones Integradas Portugal
DS Docta Complutense
RD 29 abr 2024