Riemann-Hilbert analysis for orthogonal polynomials

被引：0

作者：

Kuijlaars, ABJ ^{[1
]}

机构：

[1] Katholieke Univ Leuven, Dept Math, B-3001 Louvain, Belgium

来源：

ORTHOGONAL POLYNOMIALS AND SPECIAL FUNCTIONS | 2003年 / 1817卷

关键词：

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This is an introduction to the asymptotic analysis of orthogonal polynomials based on the steepest descent method for Riemann-Hilbert problems of Deift and Zhou. We consider in detail the polynomials that are orthogonal with respect to the modified Jacobi weight (1 - x)(alpha)(1 + x)(beta)h(x) on [-1, 1] where alpha,beta > -1 and h is real analytic and positive on [-1, 1]. These notes are based on joint work with Kenneth McLaughlin, Walter Van Assche and Maarten Vanlessen.

引用

页码：167 / 210

页数：44

共 50 条

[1] Riemann-Hilbert problems for multiple orthogonal polynomials
Van Assche, W
Geronimo, JS
Kuijlaars, ABJ
[J]. SPECIAL FUNCTIONS 2000: CURRENT PERSPECTIVE AND FUTURE DIRECTIONS, 2001, 30 : 23 - 59
[2] Riemann-Hilbert methods in the theory of orthogonal polynomials
Deift, Percy
[J]. SPECTRAL THEORY AND MATHEMATICAL PHYSICS: A FESTSCHRIFT IN HONOR OF BARRY SIMON'S 60TH BIRTHDAY: ERGODIC SCHRODINGER OPERATORS, SINGULAR SPECTRUM, ORTHOGONAL POLYNOMIALS, AND INVERSE SPECTRAL THEORY, 2007, 76 : 715 - 740
[3] Orthogonal trigonometric polynomials: Riemann-Hilbert analysis and relations with OPUC
Du, Zhihua
Du, Jinyuan
[J]. ASYMPTOTIC ANALYSIS, 2012, 79 (1-2) : 87 - 132
[4] Riemann-Hilbert analysis for Jacobi polynomials orthogonal on a single contour
Martínez-Finkelshtein, A
Orive, R
[J]. JOURNAL OF APPROXIMATION THEORY, 2005, 134 (02) : 137 - 170
[5] ASYMPTOTICS OF ORTHOGONAL POLYNOMIALS VIA THE RIEMANN-HILBERT APPROACH
Wong, R.
Zhao Yuqiu
[J]. ACTA MATHEMATICA SCIENTIA, 2009, 29 (04) : 1005 - 1034
[6] Soft Riemann-Hilbert problems and planar orthogonal polynomials
Hedenmalm, Haakan
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2024, 77 (04) : 2413 - 2451
[7] A Riemann-Hilbert approach to asymptotic questions for orthogonal polynomials
Deift, P
Kriecherbauer, T
McLaughlin, KTR
Venakides, S
Zhou, X
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2001, 133 (1-2) : 47 - 63
[8] Riemann-Hilbert problem for bi-orthogonal polynomials
Kapaev, AA
[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2003, 36 (16): : 4629 - 4640
[9] The Global Parametrix in the Riemann-Hilbert Steepest Descent Analysis for Orthogonal Polynomials
Arno B. J. Kuijlaars
Man Yue Mo
[J]. Computational Methods and Function Theory, 2011, 11 : 161 - 178
[10] The Global Parametrix in the Riemann-Hilbert Steepest Descent Analysis for Orthogonal Polynomials
Kuijlaars, Arno B. J.
Mo, Man Yue
[J]. COMPUTATIONAL METHODS AND FUNCTION THEORY, 2011, 11 (01) : 161 - 178

← 1 2 3 4 5 →