Approximation of classes of Poisson integrals by rectangular Fejér means

被引：0

作者：

Rovenska, Olga ^{[1
]}

机构：

[1] NAS Ukraine, Dept Theory Funct, Inst Math, Kyiv, Ukraine

来源：

FRONTIERS IN APPLIED MATHEMATICS AND STATISTICS | 2024年 / 10卷

关键词：

linear method of approximation; extremal problem of approximation theory; Poisson integral; Fej & eacute; r mean; exact asymptotic; SUMMABILITY;

D O I：

10.3389/fams.2024.1437247

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The article is devoted to the problem of approximation of classes of periodic functions by rectangular linear means of Fourier series. Asymptotic equalities are found for upper bounds of deviations in the uniform metric of rectangular Fej & eacute;r means on classes of periodic functions of several variables generated by sequences that tend to zero at the rate of geometric progression. In one-dimensional cases, these classes consist of Poisson integrals, namely functions that can be regularly extended in the fixed strip of a complex plane.

引用

页数：5

共 20 条

[11] On the maximal operators of Walsh-Kaczmarz-Fej,r means
Tephnadze, George
PERIODICA MATHEMATICA HUNGARICA, 2013, 67 (01) : 33 - 45
[12] Almost Everywhere Strong Summability of Fej,r Means of Rectangular Partial Sums of Two-dimensional Walsh-Fourier Series
Goginava, U.
JOURNAL OF CONTEMPORARY MATHEMATICAL ANALYSIS-ARMENIAN ACADEMY OF SCIENCES, 2018, 53 (02): : 100 - 112
[13] On series arising from the approximation of periodic differentiable functions by Poisson integrals
Zastavnyi, V. P.
MATHEMATICAL NOTES, 2009, 86 (3-4) : 469 - 482
[14] On series arising from the approximation of periodic differentiable functions by Poisson integrals
V. P. Zastavnyi
Mathematical Notes, 2009, 86
[15] Approximation of Poisson integrals by de la Vallée Poussin sums
Serdyuk A.S.
Ukrainian Mathematical Journal, 2004, 56 (1) : 122 - 134
[16] Asymptotic behavior of best approximations of classes of Poisson integrals of functions from Hω
Serdyuk, A. S.
Sokolenko, I. V.
JOURNAL OF APPROXIMATION THEORY, 2011, 163 (11) : 1692 - 1706
[17] Poisson Integrals as a (C0) Semigroup on the Banach Space L~p(R~n) (1
刘尚平
ChineseScienceBulletin, 1993, (17) : 1414 - 1416
[18] POISSON INTEGRALS AS A (CO) SEMIGROUP ON THE BANACH-SPACE L(P)(R(N))(1-LESS-THAN-P-LESS-THAN+INFINITY)
LIU, SP
CHINESE SCIENCE BULLETIN, 1993, 38 (17): : 1414 - 1416
[19] DEGREE OF APPROXIMATION OF A FUNCTION BELONGING TO WEIGHTED (L-r, xi(t)) CLASS BY (C, 1)(E, q) MEANS
Nigam, Hare Krishna
TAMKANG JOURNAL OF MATHEMATICS, 2011, 42 (01): : 31 - 37
[20] Approximation of Conjugate of Functions belonging to Lip alpha Class and W(L-r, xi(t)) Class by Product Means of Conjugate Series of Fourier Series
Nigam, H. K.
Sharma, Kusum
EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 2011, 4 (03): : 276 - 286

← 1 2 →