A Generalized Translation Operator Generated by the Sinc Function on an Interval

被引：0
|
作者：
Arestov, V. V. [1 ,2 ]
Deikalova, M. V. [1 ,2 ]
机构：
[1] Ural Fed Univ, Ekaterinburg 620000, Russia
[2] Russian Acad Sci, Ural Branch, Krasovskii Inst Math & Mech, Ekaterinburg 620108, Russia
来源：
PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS | 2023年 / 323卷 / SUPPL 1期
关键词：
generalized translation; sinc function; inequality of different metrics; L-Q-NORM; UNIFORM NORM; ALGEBRAIC POLYNOMIALS; NIKOLSKII INEQUALITY; WEIGHT; METRICS;
D O I：
10.1134/S0081543823060032
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We discuss the properties of the generalized translation operator generated by the system of functions S = {( sin k pi x)/(k pi x)}(k=1)infinity in the spaces L-q = L-q((0, 1),v), q >= 1, on the interval (0, 1) with the weight.(x) = x(2). We find an integral representation of this operator and study its norm in the spaces L-q, 1 <= q <= infinity. The translation operator is applied to the study of Nikol'skii's inequality between the uniform norm and the Lq-norm of polynomials in the system S.
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页码：S32 / S52
页数：21
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