Vector interpretation of the matrix orthogonality on the real line
Classical Analysis and ODEs
2009-10-12 v2
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.
Keywords
Cite
@article{arxiv.0910.1737,
title = {Vector interpretation of the matrix orthogonality on the real line},
author = {A. Branquinho and F. Marcellán and A. Mendes},
journal= {arXiv preprint arXiv:0910.1737},
year = {2009}
}