Relative asymptotics for orthogonal matrix polynomials

  • Branquinho A
  • Marcellán F
  • Mendes A
  • 5


    Mendeley users who have this article in their library.
  • 2


    Citations of this article.


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. © 2012 Elsevier Ltd. All rights reserved.

Author-supplied keywords

  • Asymptotic results
  • Linear functional
  • Matrix orthogonal polynomials
  • Nevai class
  • Recurrence relation
  • Tridiagonal operator

Get free article suggestions today

Mendeley saves you time finding and organizing research

Sign up here
Already have an account ?Sign in

Find this document


Cite this document

Choose a citation style from the tabs below

Save time finding and organizing research with Mendeley

Sign up for free