RT Journal Article
T1 Riemann–Hilbert problems, matrix orthogonal polynomialsand discrete matrix equations with singularity confinement
A1 Cassatella-Contra, Giovanni A.
A1 Mañas Baena, Manuel Enrique
AB n this paper, matrix orthogonal polynomials in the real line are described in terms of a RiemannHilbert problem. This approach provides an easy derivation of discrete equations for the corresponding matrix recursion coefficients. The discrete equation is explicitly derived in the matrix Freud case, associated with matrix quartic potentials. It is shown that, when the initial condition and the measure are simultaneously triangularizable, this matrix discrete equation possesses the singularity confinement property, independently if the solution under consideration is given by the recursion coefficients to quartic Freud matrix orthogonal polynomials or not.
PB Wiley-Blackwell
SN 0022-2526
YR 2012
FD 2012-04
LK https://hdl.handle.net/20.500.14352/44696
UL https://hdl.handle.net/20.500.14352/44696
LA eng
NO Wiley-Blackwell.The authors thanks economical support from the Spanish Ministerio de Ciencia e Innovación, research project FIS2008-00200. GAC acknowledges the support of the grant Universidad Complutense de Madrid. Finally, MM reckons illuminating discussions with Dr. Mattia Cafasso in relation with orthogonality and singularity confinement, and both authors are grateful to Prof. Gabriel Álvarez Galindo for several discussions and for the experimental confirmation, via Mathematica, of the existence of the confinement of singularities in the 2 × 2 case.
NO Ministerio de Ciencia e Innovación, Spain
NO Universidad Complutense de Madrid
DS Docta Complutense
RD 16 abr 2025