Algebraic theory of multiple orthogonal polynomials

• Autor(es): Branquinho, A. ; Cotrim, L. ; Moreno, A. Foulquié
• Data: 2009
• Identificador Persistente: http://hdl.handle.net/10316/11180
• Origem: Estudo Geral - Universidade de Coimbra
• Assunto(s): Multiple orthogonal polynomials; Hermite-Pad´e approximants; Block tridiagonal operator; Favard type theorem
• Tipo de Documento: Preprint
• Idioma: Inglês

Descrição

In this work we present an algebraic theory of multiple orthogonal polynomials. Our departure point is the three term recurrence relation, with matrix coefficients, satisfied by a sequence of vector multiple orthogonal polynomials. We give some characterizations of multiple orthogonal polynomials including recurrence relations, a Favard type theorem and a Christoffel-Darboux type formulas. An reinterpretation of the problems of Hermite-Pad´e approximation is presented.