Vector Interpretation of the Matrix Orthogonality on the Real Line

Branquinho, A.; Marcellán, F.; Mendes, A.

http://hdl.handle.net/10400.8/14518

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Vector interpretation of the matrix orthogonality on the real line.pdf	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.	291.42 KB	Adobe PDF	Download

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Authors

Branquinho, A.

Marcellán, F.

Mendes, A.

Abstract(s)

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.

Description

Fonte: https://arxiv.org/abs/0910.1737

Keywords

Matrix orthogonal polynomials problems of Hermite-Pad´e linear func- tional recurrence relation tridiagonal operator Favard theorem asymptotic results Nevai class

URI

http://hdl.handle.net/10400.8/14518

Citation

Branquinho, Amílcar & Marcellán, Francisco & Mendes, A.. (2009). Vector Interpretation of the Matrix Orthogonality on the Real Line. Acta Applicandae Mathematicae. DOI: https://doi.org/112. 10.1007/s10440-010-9577-3.