Resurgence relation and global asymptotic analysis of orthogonal polynomials via the Riemann-Hilbert approach

被引：1

作者：

Xu ShuaiXia ^{[1
]}

Zhao YuQiu ^{[1
]}

机构：

[1] Sun Yat Sen Univ, Zhongshan Univ, Dept Math, Guangzhou 510275, Guangdong, Peoples R China

来源：

SCIENCE CHINA-MATHEMATICS | 2011年 / 54卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Riemann-Hilbert approach; resurgence relation; uniform asymptotics; orthogonal polynomials; Hermite polynomials; Airy function; UNIFORM ASYMPTOTICS; EXPANSIONS;

D O I：

10.1007/s11425-010-4151-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A global asymptotic analysis of orthogonal polynomials via the Riemann-Hilbert approach is presented, with respect to the polynomial degree. The domains of uniformity are described in certain phase variables. A resurgence relation within the sequence of Riemann-Hilbert problems is observed in the procedure of derivation. Global asymptotic approximations are obtained in terms of the Airy function. The system of Hermite polynomials is used as an illustration.

引用

页码：661 / 679

页数：19

共 50 条

[1] Resurgence relation and global asymptotic analysis of orthogonal polynomials via the Riemann-Hilbert approach
XU ShuaiXia & ZHAO YuQiu* Department of Mathematics
Science China(Mathematics), 2011, 54 (04) : 661 - 679
[2] Resurgence relation and global asymptotic analysis of orthogonal polynomials via the Riemann-Hilbert approach
ShuaiXia Xu
YuQiu Zhao
Science China Mathematics, 2011, 54 : 661 - 679
[3] ASYMPTOTICS OF ORTHOGONAL POLYNOMIALS VIA THE RIEMANN-HILBERT APPROACH
Wong, R.
Zhao Yuqiu
ACTA MATHEMATICA SCIENTIA, 2009, 29 (04) : 1005 - 1034
[4] ASYMPTOTICS OF ORTHOGONAL POLYNOMIALS VIA THE RIEMANN-HILBERT APPROACH
赵育求
ActaMathematicaScientia, 2009, 29 (04) : 1005 - 1034
[5] A Riemann-Hilbert approach to asymptotic questions for orthogonal polynomials
Deift, P
Kriecherbauer, T
McLaughlin, KTR
Venakides, S
Zhou, X
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2001, 133 (1-2) : 47 - 63
[6] THE RIEMANN-HILBERT APPROACH TO GLOBAL ASYMPTOTICS OF DISCRETE ORTHOGONAL POLYNOMIALS WITH INFINITE NODES
Ou, Chunhua
Wong, R.
ANALYSIS AND APPLICATIONS, 2010, 8 (03) : 247 - 286
[7] Global asymptotics of hermite polynomials via Riemann-Hilbert approach
Wong, R.
Zhang, L.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2007, 7 (03): : 661 - 682
[8] UNIFORM ASYMPTOTICS OF A SYSTEM OF SZEGO CLASS POLYNOMIALS VIA THE RIEMANN-HILBERT APPROACH
Zhou, Jian-Rong
Xu, Shuai-Xia
Zhao, Yu-Qiu
ANALYSIS AND APPLICATIONS, 2011, 9 (04) : 447 - 480
[9] Plancherel-Rotach type asymptotics of the sieved Pollaczek polynomials via the Riemann-Hilbert approach
Wu, Xiao-Bo
Lin, Yu
Xu, Shuai-Xia
Zhao, Yu-Qiu
JOURNAL OF APPROXIMATION THEORY, 2016, 208 : 21 - 58
[10] Introduction to asymptotics for orthogonal polynomials via Riemann-Hilbert methods
McLaughlin, K
LAREDO LECTURES ON ORTHOGONAL POLYNOMIALS AND SPECIAL FUNCTIONS, 2004, : 85 - 109

← 1 2 3 4 5 →