Best Linear Approximation Methods for Some Classes of Analytic Functions on the Unit Disk

被引：3

作者：

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

Langarshoev, M. R. ^{[2
]}

机构：

[1] Tajik Natl Univ, Univ Cent Asia, Dushanbe, Tajikistan

[2] Tajik Natl Univ, Dushanbe, Tajikistan

来源：

SIBERIAN MATHEMATICAL JOURNAL | 2019年 / 60卷 / 06期

关键词：

best linear approximation methods; modulus of continuity; weighted Bergman space; majorant; n-widths; best coding method; EXACT VALUES; WIDTHS; BALL;

D O I：

10.1134/S0037446619060181

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Considering Banach Hardy spaces and weighted Bergman spaces, we find the sharp values of the Bernstein, Kolmogorov, Gelfand, and linear n-widths for the classes of analytic functions on the unit disk whose moduli of continuity of the rth derivatives averaged with weight are majorized by a given function satisfying some constraints.

引用

页码：1101 / 1108

页数：8

共 50 条

[41] On best approximation of classes by radial functions
Maiorov, V
JOURNAL OF APPROXIMATION THEORY, 2003, 120 (01) : 36 - 70
[42] The best approximation to analytic functions.
Achyeser, N
COMPTES RENDUS DE L ACADEMIE DES SCIENCES DE L URSS, 1938, 18 : 241 - 244
[43] BEST APPROXIMATION METHODS AND WIDTHS FOR SOME CLASSES OF FUNCTIONS IN Hq,ρ, 1 ≤ q ≤ ∞, 0 < ρ ≤ 1
Shabozov, M. Sh.
Yusupov, G. A.
SIBERIAN MATHEMATICAL JOURNAL, 2016, 57 (02) : 369 - 376
[44] On best rational approximation of analytic functions
Prokhorov, VA
JOURNAL OF APPROXIMATION THEORY, 2005, 133 (02) : 284 - 296
[45] CONCERNING SOME SUBSETS OF FUNCTIONS ANALYTIC ON UNIT DISK - PRELIMINARY REPORT
RYAN, DE
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1973, 20 (07): : A661 - A661
[46] On the Best Approximation of Functions Analytic in the Disk in the Weighted Bergman Space B2,μ
Langarshoev, M. R.
RUSSIAN MATHEMATICS, 2024, 68 (06) : 21 - 29
[47] Best Linear Methods of Approximation of Functions of the Hardy Class Hp
V. V. Savchuk
Ukrainian Mathematical Journal, 2003, 55 (7) : 1110 - 1118
[48] APPROXIMATION OF ANALYTIC-FUNCTIONS IN SOME FUNCTIONAL SPACES AND THE RATIONAL APPROXIMATION OF FUNCTIONS FROM HARDY-CLASSES
DOVGOSHEI, AA
MATHEMATICAL NOTES, 1993, 53 (1-2) : 158 - 162
[49] Best linear approximation methods for functions of Taikov classes in the Hardy spaces Hq,ρ, q ≥ 1, 0 < ρ ≤ 1
S. B. Vakarchuk
V. I. Zabutnaya
Mathematical Notes, 2009, 85 : 322 - 327
[50] Approximation of subharmonic functions in the unit disk
Chyzhykov, I. E.
JOURNAL OF MATHEMATICAL PHYSICS ANALYSIS GEOMETRY, 2008, 4 (02) : 211 - 236

← 1 2 3 4 5 →