A new approach to ratio asymptotics for orthogonal polynomials

被引：7
|
作者：
Simanek, Brian [1 ]
机构：
[1] CALTECH, Pasadena, CA 91125 USA
来源：
JOURNAL OF SPECTRAL THEORY | 2012年 / 2卷 / 04期
基金：
美国国家科学基金会;
关键词：
Orthogonal polynomials; ratio asymptotics; relative asymptotics; regular measures; RELATIVE ASYMPTOTICS; WEAK-CONVERGENCE; CD KERNELS;
D O I：
10.4171/JST/34
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We use a non-linear characterization of orthonormal polynomials due to Saff in order to show that the behavior of orthonormal polynomials is uniquely determined by the normalization and leading coefficient. Several applications of this result are also discussed. One of our main theorems is that for regular measures on the closed unit disk - including, but not limited to the unit circle - one has ratio asymptotics along a sequence of asymptotic density 1.
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页码：373 / 395
页数：23
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