On the best linear approximation methods and the widths of certain classes of analytic functions

被引：8

作者：

Vakarchuk, SB ^{[1
]}

机构：

[1] Natl Acad Sci Ukraine, Inst Geotech Mech, Dnepropetrovsk, Ukraine

来源：

MATHEMATICAL NOTES | 1999年 / 65卷 / 1-2期

关键词：

linear approximation of analytic functions; linear n-width; Gelfand n-width; Kolmogorov n-width; Bernstein n-width; function set; Hardy space; K-functional;

D O I：

10.1007/BF02679811

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We discuss the best linear approximation methods in the Hardy space H-q, q greater than or equal to 1, for classes of analytic functions studied by N. Ainulloev; these are generalizations (in a certain sense) of function sets introduced by L. V. Taikov. The exact values of their linear and Gelfand n-widths are obtained. The exact values of the Kolmogorov and Bernstein n-widths of classes of analytic (in \z\ < 1) functions whose boundary K-functionals are majorized by a prescribed functions are also obtained.

引用

页码：153 / 158

页数：6

共 12 条

[1] AINULLOEV N, 1986, GEOMETRIC PROBLEMS F, P91
[2] [Anonymous], 1959, TRIGONOMETRIC SERIES
[3] BERGH J, 1976, INTERPOLATION SPAC I
[4] Farkov YA., 1990, USP MAT NAUK, V45, P197
[5] THE N-WIDTH OF THE UNIT BALL OF HQ
FISHER, SD
STESSIN, MI
[J]. JOURNAL OF APPROXIMATION THEORY, 1991, 67 (03) : 347 - 356
[6] ON SOME APPROXIMATION PROPERTIES OF REAL HARDY-SPACES (0 LESS-THAN P LESS-THAN-OR-EQUAL-TO 1)
OSWALD, P
[J]. JOURNAL OF APPROXIMATION THEORY, 1984, 40 (01) : 45 - 65
[7] Pinkus A., 1985, N WIDTHS APPROXIMATI
[8] Schumaker L., 1981, SPLINE FUNCTIONS BAS
[9] SHIKHALIEV NI, 1975, DOKL AKAD NAUK AZER, V31, P9
[10] TAIKOV AV, 1977, MAT ZAMETKI, V22, P285

← 1 2 →