Ratio and relative asymptotics of polynomials orthogonal with respect to varying Denisov-type measures

JOURNAL OF APPROXIMATION THEORY

卷:139

Article

Rolania, DB ; Ysern, BDLC ; Lagomasino, GL

关键词: varying measures;    ratio asymptotics;    relative asymptotics;    Nikishin system;    Hermite-Pade orthogonal polynomials;   

DOI  :  10.1016/j.jat.2005.08.006

来源: Elsevier

【 摘 要 】

Let it be a finite positive Borel measure with compact support consisting of an interval [c, d] subset of R plus a set of isolated points in R\[c, d], such that mu' > 0 almost everywhere on [c. d]. Let {w(2n)}, n is an element of Z(+). be a sequence of polynomials, deg w(2n) <= 2n, with real coefficients whose zeros lie outside the smallest interval containing the support of mu. We prove ratio and relative asymptotics of sequences of orthogonal polynomials with respect to varying measures of the form d mu/w(2n). In particular, we obtain an analogue for varying measures of Denisov's extension of Rakhmanov's theorem on ratio asymptotics. These results on varying measures are applied to obtain ratio asymptotics for orthogonal polynomials with respect to fixed measures on the unit circle and for multi-orthogonal polynomials in which the measures involved are of the type described above. (C) 2005 Elsevier Inc. All rights reserved.

【 授权许可】

Free