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arXiv · 1412.8580

Weights with both absolutely continuous and discrete components: Asymptotics via the Riemann-Hilbert approach

Xiao-Bo Wu·Yu Lin·Shuai-Xia Xu·Yu-Qiu Zhao
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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.

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Xiao-Bo Wu, Yu Lin, Shuai-Xia Xu, Yu-Qiu Zhao. 2014-12-30. Weights with both absolutely continuous and discrete components: Asymptotics via the Riemann-Hilbert approach. https://arxiv.org/abs/1412.8580

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