THE SMALLEST EIGENVALUE OF THE ILL-CONDITIONED HANKEL MATRICES ASSOCIATED WITH A SEMI-CLASSICAL HERMITE WEIGHT

被引：0

作者：

Wang, Yuxi ^{[1
]}

Zhu, Mengkun ^{[2
]}

Chen, Yang

机构：

[1] Univ Macau, Fac Sci & Technol, Dept Math, Ave Univ, Taipa, Macau, Peoples R China

[2] Qilu Univ Technol, Shandong Acad Sci, Sch Math & Stat, Jinan 250353, Peoples R China

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2023年 / 151卷 / 12期

基金：

中国国家自然科学基金;

关键词：

Orthogonal polynomials; Hankel matrices; smallest eigenvalue; ORTHOGONAL POLYNOMIALS; GAUSSIAN WEIGHT; DETERMINANT;

D O I：

10.1090/proc/16554

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the asymptotic behavior of the smallest eigenvalue & lambda;N, of the (N + 1) x (N + 1) Hankel matrix MN = (& mu;j+k)0 & LE;j,k & LE;N generated by the semi-classical Hermite weight w(z, t) = |z|& lambda; exp (-z2 +tz) , z, t & ISIN; R, & lambda; > -1. An asymptotic expression of the orthonormal polynomi-als PN(z) with the semi-classical Hermite weight w(z, t) is established as N tends to infinity. Based on the orthonormal polynomials PN(z), we obtain the specific asymptotic formulas of & lambda;N.

引用

页码：5345 / 5352

页数：8

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