Please use this identifier to cite or link to this item:
https://hdl.handle.net/10316/13638
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. | URI: | https://hdl.handle.net/10316/13638 | Rights: | openAccess |
Appears in Collections: | FCTUC Matemática - Vários |
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Vector interpretation of the matrix orthogonality.pdf | 282.71 kB | Adobe PDF | View/Open |
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