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

authors

  • ALVAREZ FERNANDEZ, CARLOS
  • FIDALGO PRIETO, ULISES
  • MA√ĎAS BAENA, MANUEL

publication date

  • May 2010

start page

  • 1

end page

  • 15

issue

  • 5 (055009)

volume

  • 26

International Standard Serial Number (ISSN)

  • 0266-5611

Electronic International Standard Serial Number (EISSN)

  • 1361-6420

abstract

  • 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.