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

IF 4.3 3区 材料科学 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC ACS Applied Electronic Materials Pub Date : 2023-07-03 DOI:10.1002/cpa.22122
Seung-Yeop Lee, Meng Yang
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引用次数: 11

摘要

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

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

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来源期刊
ACS Applied Electronic Materials
ACS Applied Electronic Materials Multiple-
CiteScore
7.20
自引率
4.30%
发文量
567
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