Weights with both absolutely continuous and discrete components: Asymptotics via the Riemann-Hilbert approach
Complex Variables
2014-12-31 v1
Abstract
We study the uniform asymptotics for the orthogonal polynomials with respect to weights composed of both absolutely continuous measure and discrete measure, by taking a special class of the sieved Pollazek Polynomials as an example. The Plancherel-Rotach type asymptotics of the sieved Pollazek Polynomials are obtained in the whole complex plane. The Riemann-Hilbert method is applied to derive the results. A main feature of the treatment is the appearance of a new band consisting of two adjacent intervals, one of which is a portion of the support of the absolutely continuous measure, the other is the discrete band.
Keywords
Cite
@article{arxiv.1412.8580,
title = {Weights with both absolutely continuous and discrete components: Asymptotics via the Riemann-Hilbert approach},
author = {Xiao-Bo Wu and Yu Lin and Shuai-Xia Xu and Yu-Qiu Zhao},
journal= {arXiv preprint arXiv:1412.8580},
year = {2014}
}
Comments
31 pages, 5 figures