Spectral transforms of measures and orthogonal polynomials on regions

被引：2

作者：

Mina-Diaz, Erwin ^{[1
]}

Simanek, Brian ^{[2
]}

机构：

[1] Univ Mississippi, Dept Math, University, MS 38677 USA

[2] Vanderbilt Univ, Dept Math, Nashville, TN 37240 USA

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2013年 / 407卷 / 02期

关键词：

Orthogonal polynomials; Strong asymptotics; Geronimus transform; Christoffel transform; Uvarov transform;

D O I：

10.1016/j.jmaa.2013.05.035

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We discuss Szego-type strong asymptotics for polynomials orthogonal over a region bounded by an analytic curve, and find necessary conditions for such asymptotics to hold on an interior neighborhood of the curve. We also prove that this property is not destroyed when the measure is perturbed by multiplication by a rational function and the addition of point masses. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：290 / 304

页数：15

共 50 条

[1] Fourier transforms of orthogonal polynomials of singular continuous spectral measures
Mantica, G
[J]. APPLICATIONS AND COMPUTATION OF ORTHOGONAL POLYNOMIALS, 1999, 131 : 153 - 163
[2] Orthogonal polynomials, spectral measures, and absolute continuity
Dombrowski, J
Pedersen, S
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1995, 65 (1-3) : 115 - 124
[3] SPECTRAL MEASURES, ORTHOGONAL POLYNOMIALS, AND ABSOLUTE CONTINUITY
DOMBROWSKI, J
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1988, 19 (04) : 939 - 943
[4] SPECTRAL MEASURES CORRESPONDING TO ORTHOGONAL POLYNOMIALS WITH UNBOUNDED RECURRENCE COEFFICIENTS
DOMBROWSKI, J
[J]. CONSTRUCTIVE APPROXIMATION, 1989, 5 (03) : 371 - 381
[5] MEASURES ORTHOGONAL TO POLYNOMIALS
BISHOP, E
[J]. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1958, 44 (03) : 278 - 280
[6] FOURIER TRANSFORMS OF ORTHOGONAL POLYNOMIALS ON THE CONE
Karaman, RabıA Aktaş
Area, Iván
[J]. arXiv,
[7] h-Transforms and Orthogonal Polynomials
Bakry, Dominique
Zribi, Olfa
[J]. IN MEMORIAM MARC YOR - SEMINAIRE DE PROBABILITES XLVII, 2015, 2137 : 157 - 185
[8] The asymptotic behaviour of the Fourier transforms of orthogonal polynomials II: LIFS measures and quantum mechanics
Mantica, Giorgio
Guzzetti, Davide
[J]. ANNALES HENRI POINCARE, 2007, 8 (02): : 301 - 336
[9] Orthogonal Polynomials Associated with Related Measures and Sobolev Orthogonal Polynomials
A.C. Berti
C.F. Bracciali
A. Sri Ranga
[J]. Numerical Algorithms, 2003, 34 : 203 - 216
[10] Orthogonal polynomials associated with related measures and Sobolev orthogonal polynomials
Berti, AC
Bracciali, CF
Ranga, AS
[J]. NUMERICAL ALGORITHMS, 2003, 34 (2-4) : 203 - 216

← 1 2 3 4 5 →