Matrix interpretation of multiple orthogonality

• Author(s): Branquinho, A. ; Cotrim, L. ; Moreno, A. Foulquié
• Date: 2008
• Persistent ID: http://hdl.handle.net/10316/11204
• Origin: Estudo Geral - Universidade de Coimbra
• Subject(s): Multiple-orthogonal polynomials; Hermite-Padé approximants; Block tridiagonal operator; Favard type theorem
• Document Type: Preprint
• Language: English

Description

In this work we give an interpretation of a (s(d + 1) + 1)-term recurrence relation in terms of type II multiple orthogonal polynomials. We rewrite this recurrence relation in matrix form and we obtain a three-term recurrence relation for vector polynomials with matrix coefficients. We present a matrix interpretation of the type II multi-ortogonality conditions. We state a Favard type theorem and the expression for the resolvent function associated to the vector of linear functionals. Finally a reinterpretation of the type II Hermite-Pad´e approximation in matrix form is given.