Rational Functions with a General Distribution of Poles on the Real Line Orthogonal with Respect to Varying Exponential Weights: I

被引：1

作者：

McLaughlin, K. T. -R. ^{[2
]}

Vartanian, A. H. ^{[1
]}

Zhou, X. ^{[3
]}

机构：

[1] Coll Charleston, Dept Math, Charleston, SC 29424 USA

[2] Univ Arizona, Dept Math, Tucson, AZ 85721 USA

[3] Duke Univ, Dept Math, Durham, NC 27708 USA

来源：

MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY | 2008年 / 11卷 / 3-4期

基金：

美国国家科学基金会;

关键词：

Asymptotics; Equilibrium measures; Orthogonal rational functions; Riemann-Hilbert problems; Variational problems; Primary; 42C05; Secondary; 30E20; 30E25; 30C15;

D O I：

10.1007/s11040-008-9042-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Orthogonal rational functions are characterized in terms of a family of matrix Riemann-Hilbert problems on R, and a related family of energy minimisation problems is presented. Existence, uniqueness, and regularity properties of the equilibrium measures which solve the energy minimisation problems are established. These measures are used to derive a family of 'model' matrix Riemann-Hilbert problems which are amenable to asymptotic analysis via the Deift-Zhou non-linear steepest-descent method.

引用

页码：187 / 364

页数：178

共 9 条

[1] Rational Functions with a General Distribution of Poles on the Real Line Orthogonal with Respect to Varying Exponential Weights: I
K. T.-R. McLaughlin
A. H. Vartanian
X. Zhou
Mathematical Physics, Analysis and Geometry, 2008, 11 : 187 - 364
[2] Orthogonal rational functions on the real half line with poles in [-∞, 0]
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[4] Zero distribution of complex orthogonal polynomials with respect to exponential weights
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[5] Asymptotics of Recurrence Relation Coefficients, Hankel Determinant Ratios, and Root Products Associated with Laurent Polynomials Orthogonal with Respect to Varying Exponential Weights
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[6] Asymptotics of recurrence relation coefficients, Hankel determinant ratios, and root products associated with Laurent polynomials orthogonal with respect to varying exponential weights
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[8] The convergence properties of orthogonal rational functions on the extended real line and analytic on the upper half plane
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INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING, 2020, 18 (05)
[9] On three-term recurrence and Christoffel-Darboux identity for orthogonal rational functions on the real line
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