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Strong Asymptotic Analysis of OLPs on the Unit Circle by Riemann-Hilbert Approach

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Analysis as a Life

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Abstract

In this article, we will deal with the asymptotics of the monic orthogonal Laurent polynomials (OLPs) on the unit circle with respect to a strictly-positive analytic weight by Riemann-Hilbert approach. We first construct a matrix Riemann-Hilbert problem (RHP) which is the Fokas-Its-Kitaev characterization. Then, the strong asymptotic formulas of OLPs are obtained by employing Deift-Zhou steepest descent analysis. Furthermore, the asymptotic formulas of the leading coefficient and the trailing coefficient are simultaneously obtained.

To Professor Heinrich Begehr on the occasion of his 80th birthday

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Acknowledgements

While the corresponding author visited Free University Berlin in summer 2005 on basis of State Scholarship Fund Award of China, our group began to explore the application of Riemann-Hilbert approach, and made a debut [3]. During that time Professor H. Begehr carefully reviewed this manuscript and offered a lot of suggestions. All the authors are very grateful to Professor H. Begehr for his long-term support and help.

This work was supported by NNSF for Young Scholars of China (No. 11001206) and NNSF (No. 11171260).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Wuhan University, Wuhan, China

    Yufeng Wang, Yifeng Lu & Jinyuan Du

  2. School of Science, Linyi University, Shandong, China

    Jinyuan Du

Authors
  1. Yufeng Wang
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  2. Yifeng Lu
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  3. Jinyuan Du
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Correspondence to Jinyuan Du .

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Editors and Affiliations

  1. Department of Economics, Belarusian State University, Minsk, Belarus

    Sergei Rogosin

  2. Mathematics Department, Yeditepe University, AtaĹźehir, Istanbul, Turkey

    Ahmet Okay Çelebi

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Wang, Y., Lu, Y., Du, J. (2019). Strong Asymptotic Analysis of OLPs on the Unit Circle by Riemann-Hilbert Approach. In: Rogosin, S., Çelebi, A. (eds) Analysis as a Life. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-02650-9_8

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