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Title: Relative asymptotics for orthogonal matrix polynomials
Authors: Branquinho, A. 
Marcellán, F. 
Mendes, A. 
Keywords: Matrix orthogonal polynomials; Linear functional; Recurrence relation; Tridiagonal operator; Asymptotic results; Nevai class
Issue Date: 2010
Publisher: Centro de Matemática da Universidade de Coimbra
Citation: Pré-Publicações DMUC. 10-09 (2010)
Serial title, monograph or event: Pré-Publicações DMUC
Issue: 10-09
Place of publication or event: Coimbra
Abstract: In this paper we study sequences of matrix polynomials that satisfy a non-symmetric recurrence relation. To study this kind of sequences we use a vector interpretation of the matrix orthogonality. In the context of these sequences of matrix polynomials we introduce the concept of the generalized matrix Nevai class and we give the ratio asymptotics between two consecutive polynomials belonging to this class. We study the generalized matrix Chebyshev polynomials and we deduce its explicit expression as well as we show some illustrative examples. The concept of a Dirac delta functional is introduced. We show how the vector model that includes a Dirac delta functional is a representation of a discrete Sobolev inner product. It also allows to reinterpret such perturbations in the usual matrix Nevai class. Finally, the relative asymptotics between a polynomial in the generalized matrix Nevai class and a polynomial that is orthogonal to a modification of the corresponding matrix measure by the addition of a Dirac delta functional is deduced.
Rights: openAccess
Appears in Collections:FCTUC Matemática - Vários

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