Vector interpretation of the matrix orthogonality on the real line

• Author(s): Branquinho, A. ; Marcellán, F. ; Mendes, A.
• Date: 2009
• Persistent ID: http://hdl.handle.net/10316/13638
• Origin: Estudo Geral - Universidade de Coimbra
• Subject(s): Matrix orthogonal polynomials; Hermite-Padé problems; Linear functional; Recurrence relation; Tridiagonal operator; Favard theorem; Nevai class
• Document Type: Preprint
• Language: English

Description

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.