Relative asymptotics for orthogonal matrix polynomials with convergent recurrence coefficients

JOURNAL OF APPROXIMATION THEORY

卷:111

Article

Yakhlef, HO ; Marcellán, F ; Piñar, MA

关键词: ratio asymptotics;    orthogonal matrix polynomials;    perturbation of matrix measure;   

DOI  :  10.1006/jath.2001.3557

来源: Elsevier

【 摘 要 】

The asymptotic behavior of gamma (n)(d beta) gamma (n)(d alpha)(-1) and P-n(x, d beta) P-n(-1)(x, d alpha) is studied. Here (gamma (n)(.))(n) are the leading coefficients of the orthonormal matrix polynomials P-n(x,.) with respect to the matrix measures d beta and d alpha which are related by d beta (u)= d alpha (u)+ Sigma (N)(k=1), M(k)delta (u - c(k)), where M-k are positive definite matrices, delta is the Dirac measure and c(k) lies outside the support of d alpha for k = 1,..., N. Finally, we deduce the asymptotic behavior of P-n(c, d beta) MPn*(c, d alpha) when d beta (u) = d alpha (u) + M delta (u - c), with M a positive definite matrix and c outside the support of d alpha. (C) 2001 Academic Press.

【 授权许可】

Free