Strong Asymptotics of Planar Orthogonal Polynomials: Gaussian Weight Perturbed by Finite Number of Point Charges

IF 3.1 1区数学 Q1 MATHEMATICS

Communications on Pure and Applied Mathematics Pub Date : 2023-07-03 DOI:10.1002/cpa.22122

Seung-Yeop Lee, Meng Yang

引用次数: 11

Abstract

We consider the orthogonal polynomial pn(z) with respect to the planar measure supported on the whole complex plane

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平面正交多项式的强渐近性:有限个数点电荷扰动的高斯权

我们考虑在整个复平面e−N|z|2∏j=1ν|z−aj|2cjdA(z) $$\begin{equation*}{{\mathrm{e}}}^{ - N|z{|}^2}\prod\limits_{j = 1}^\nu {|z - {a}_j{|}^{2{c}_j}} {\mathrm{d}}A(z)\end{equation*}$$上支持的平面测度的正交多项式pn(z)，其中dA是平面的勒贝格测度，N是一个正常数，{c1，…}，cν是大于- 1的非零实数，{a1，…}，D≠{0}$\{ {a}_1, \ldots ,{a}_\nu \} \subset \mathbb{D}\backslash \{ 0\} $是单位圆盘内的不同点。在n/ n = 1和n→∞的尺度极限下，得到了多项式pn(z)的强渐近性。我们证明了根的支持收敛于我们所说的“多重塞格尔曲线”，这是一条具有ν + 1分量的连通曲线。我们将非线性最陡下降方法[9,10]应用于[22]中大小为(ν + 1) × (ν + 1)的矩阵Riemann - Hilbert问题。©2023 Wiley期刊有限责任公司

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Communications on Pure and Applied Mathematics 数学-数学

CiteScore

6.70

自引率

3.30%

发文量

审稿时长

>12 weeks

期刊介绍： Communications on Pure and Applied Mathematics (ISSN 0010-3640) is published monthly, one volume per year, by John Wiley & Sons, Inc. © 2019. The journal primarily publishes papers originating at or solicited by the Courant Institute of Mathematical Sciences. It features recent developments in applied mathematics, mathematical physics, and mathematical analysis. The topics include partial differential equations, computer science, and applied mathematics. CPAM is devoted to mathematical contributions to the sciences; both theoretical and applied papers, of original or expository type, are included.