Continuity of Weighted Operators, Muckenhoupt Ap Weights, and Steklov Problem for Orthogonal Polynomials

被引：2

作者：

Alexis, Michel ^{[1
]}

Aptekarev, Alexander ^{[2
]}

Denisov, Sergey ^{[1
,2
]}

机构：

[1] Univ Wisconsin, Dept Math, 480 Lincoln Dr, Madison, WI 53706 USA

[2] Russian Acad Sci, Keldysh Inst Appl Math, Miusskaya Pl 4, Moscow 125047, Russia

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2022年 / 2022卷 / 08期

基金：

美国国家科学基金会;

关键词：

D O I：

10.1093/imrn/rnaa249

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider weighted operators acting on L-p(R-d) and show that they depend continuously on the weight w is an element of A(p) (R-d) in the operator topology. Then, we use this result to estimate L-w(p)(T) norm of polynomials orthogonal on the unit circle when the weight w belongs to Muckenhoupt class A(2)(T) and p > 2. The asymptotics of the polynomial entropy is obtained as an application.

引用

页码：5935 / 5972

页数：38

共 12 条

[1] SOME ESTIMATES FOR ORTHOGONAL POLYNOMIALS AND ON STEKLOV PROBLEM
GERONIMUS, JL
DOKLADY AKADEMII NAUK SSSR, 1977, 236 (01): : 14 - 17
[2] ON THE STEKLOV,V.A. PROBLEM IN THE THEORY OF ORTHOGONAL POLYNOMIALS
RAKHMANOV, EA
DOKLADY AKADEMII NAUK SSSR, 1980, 254 (04): : 802 - 806
[3] V.A. Steklov’s problem of estimating the growth of orthogonal polynomials
A. I. Aptekarev
S. A. Denisov
D. N. Tulyakov
Proceedings of the Steklov Institute of Mathematics, 2015, 289 : 72 - 95
[4] Weighted shift operators, orthogonal polynomials and chain sequences
Rupert Lasser
Josef Obermaier
Acta Scientiarum Mathematicarum, 2020, 86 : 331 - 342
[5] Weighted shift operators, orthogonal polynomials and chain sequences
Lasser, Rupert
Obermaier, Josef
ACTA SCIENTIARUM MATHEMATICARUM, 2020, 86 (1-2): : 331 - 342
[6] V. A. Steklov's Problem of Estimating the Growth of Orthogonal Polynomials
Aptekarev, A. I.
Denisov, S. A.
Tulyakov, D. N.
PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 2015, 289 (01) : 72 - 95
[7] Notes on orthogonal polynomials for exponential weights (root-distances.: Weighted lebesgue function)
Vertesi, P.
ACTA MATHEMATICA HUNGARICA, 2008, 119 (04) : 381 - 392
[8] Differential equations for multiple orthogonal polynomials with respect to classical weights: raising and lowering operators
Coussement, J.
Van Assche, W.
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2006, 39 (13): : 3311 - 3318
[9] Notes on orthogonal polynomials for exponential weights (Root-distances. Weighted Lebesgue function)
P. Vértesi
Acta Mathematica Hungarica, 2008, 119 : 381 - 392
[10] POSITIVE CONVERGENT APPROXIMATION OPERATORS ASSOCIATED WITH ORTHOGONAL POLYNOMIALS FOR WEIGHTS ON THE WHOLE REAL LINE
KNOPFMACHER, A
JOURNAL OF APPROXIMATION THEORY, 1986, 46 (02) : 182 - 203

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