On the Best Approximation in the Mean of Functions of a Complex Variable by Fourier Series in the Bergman Space

被引：4

作者：

Shabozov, M. Sh. ^{[1
]}

Khuromonov, Kh. M. ^{[1
]}

机构：

[1] Tajik Natl Univ, 17 Rudaki Ave, Dushanbe 734025, Tajikistan

来源：

RUSSIAN MATHEMATICS | 2020年 / 64卷 / 02期

关键词：

supremum; module of continuity; Jacks on-Stechkin inequality; n-widths; K-functional;

D O I：

10.3103/S1066369X20020073

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In a simply connected domain of the complex plane, we consider the problem of mean-square approximation of analytic functions by Fourier series in orthogonal systems. For some classes of functions analytic in the unit disk, the supremums of mean-square approximation given by special modules of continuity are found.

引用

页码：66 / 83

页数：18

共 12 条

[1] Sharp estimates for the convergence rate of Fourier series of complex variable functions in L 2(D, p(z)) [J].

Abilov, V. A. ;

Abilova, F. V. ;

Kerimov, M. K. .

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2010, 50 (06) :946-950

[2]

Bergh J., 1976, GRUNDLEHREN MATH WIS

[3] K-FUNCTIONALS AND BEST POLYNOMIAL-APPROXIMATION IN WEIGHTED LP(R) [J].

DITZIAN, Z ;

TOTIK, V .

JOURNAL OF APPROXIMATION THEORY, 1986, 46 (01) :38-41

[4]

Ditzian Z., 1987, Moduli of Smoothness

[5]

Pinkus A., 1985, N WIDTHS APPROXIMATI, V7, DOI DOI 10.1007/978-3-642-69894-1

[6]

[Шабозов Мирганд Шабозович Shabozov Mirgand Shabozovich], 2018, [Владикавказский математический журнал, Vladikavkazskii matematicheskii zhurnal], V20, P86, DOI 10.23671/VNC.2018.1.11400

[7]

Shevchuk LA, 1992, APPROXIMATION POLYNO

[8]

Smirnov V. I., 1968, Functions of a Complex Variable (Constructive Theory)

[9]

Tikhomirov V. M., 1976, SOME QUESTIONS APPRO

[10] Mean approximation of functions on the real axis by algebraic polynomials with Chebyshev-Hermite weight and widths of function classes [J].

Vakarchuk, S. B. .

MATHEMATICAL NOTES, 2014, 95 (5-6) :599-614

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