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Title: Vector interpretation of the matrix orthogonality on the real line
Authors: Branquinho, A. 
Marcellán, F. 
Mendes, A. 
Keywords: Matrix orthogonal polynomials; Hermite-Padé problems; Linear functional; Recurrence relation; Tridiagonal operator; Favard theorem; Nevai class
Issue Date: 2009
Publisher: Centro de Matemática da Universidade de Coimbra
Citation: Pré-Publicações DMUC. 09-41 (2009)
Serial title, monograph or event: Pré-Publicações DMUC
Issue: 09-41
Place of publication or event: Coimbra
Abstract: In this paper we study sequences of vector orthogonal polynomials. The vector orthogonality presented here provides a reinterpretation of what is known in the literature as matrix orthogonality. These systems of orthogonal polynomials satisfy three-term recurrence relations with matrix coefficients that do not obey to any type of symmetry. In this sense the vectorial reinterpretation allows us to study a non-symmetric case of the matrix orthogonality. We also prove that our systems of polynomials are indeed orthonormal with respect to a complex measure of orthogonality. Approximation problems of Hermite-Pad´e type are also discussed. Finally, a Markov’s type theorem is presented.
Rights: openAccess
Appears in Collections:FCTUC Matemática - Vários

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