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arXiv · 0910.1737

Vector interpretation of the matrix orthogonality on the real line

A. Branquinho·F. Marcellán·A. Mendes
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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-Padé type are also discussed. Finally, a Markov's type theorem is presented.

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A. Branquinho, F. Marcellán, A. Mendes. 2009-10-12. Vector interpretation of the matrix orthogonality on the real line. https://arxiv.org/abs/0910.1737

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