Algebraic theory of multiple orthogonal polynomials

• Author(s): Branquinho, A. ; Cotrim, L. ; Moreno, A. Foulquié
• Date: 2009
• Persistent ID: http://hdl.handle.net/10316/11180
• Origin: Estudo Geral - Universidade de Coimbra
• Subject(s): Multiple orthogonal polynomials; Hermite-Pad´e approximants; Block tridiagonal operator; Favard type theorem
• Document Type: Preprint
• Language: English

Description

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.