Riemann–Hilbert problems, matrix orthogonal polynomials and discrete matrix equations with singularity confinement

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,...

Descripción completa

Detalles Bibliográficos
Autores: Cassatella-Contra, Giovanni A., Mañas Baena, Manuel Enrique
Tipo de recurso: artículo
Fecha de publicación:2012
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/44696
Acceso en línea:https://hdl.handle.net/20.500.14352/44696
Access Level:acceso abierto
Palabra clave:51-73
2nd-Order differential-equations
Painleve equations
Formulas
Física-Modelos matemáticos
Física matemática
Descripción
Sumario: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.