Relative asymptotics for orthogonal matrix polynomials with unbounded recurrence coefficients

Abstract

We study the asymptotic behavior of the ratio of two sequences of orthonormal matrix polynomials P _n (with unbounded three-term recurrence coefficients) and [Ptilde] _n , which are associated, respectively, to a matrix of measures and its perturbation by the addition of a Dirac matrix measure.

Keywords:

• Orthogonal matrix polynomials
• Perturbation of varying matrix of measures
• Asymptotic behavior

Acknowledgements

I thank José L. López (Universidad Pública de Navarra) for his hospitality during the preparation of this work and F. Marcellán (Universidad Carlos III de Madrid) for some fruitful discussions and useful suggestions. This work has been supported by the University Pública de Navarra and the Government of Navarra (Res. 92/2002).