Approximation of Periodic Functions of Many Variables in Metric Spaces by Piecewise-Constant Functions

被引：1

作者：

Agoshkova, T. A. ^{[1
]}

机构：

[1] Dnepropetrovsk Natl Univ Railway Transport, Dnepropetrovsk, Ukraine

来源：

UKRAINIAN MATHEMATICAL JOURNAL | 2014年 / 65卷 / 10期

关键词：

Periodic Function; English Translation; Step Function; Function Reference; Equidistant Point;

D O I：

10.1007/s11253-014-0871-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove the direct and inverse Jackson- and Bernstein-type theorems for averaged approximations of periodic functions of many variables by piecewise-constant functions with uniform partition of the period torus in metric spaces with integral metric given by a function psi of the type of modulus of continuity.

引用

页码：1447 / 1459

页数：13

共 50 条

[21] Approximation by piecewise constant functions on a square
Kochurov, AS
MATHEMATICAL NOTES, 2004, 75 (3-4) : 553 - 562
[22] APPROXIMATION OF DIFFERENTIABLE FUNCTIONS OF MANY VARIABLES BY FOURIER SUMS IN LP METRIC
NIKOLSKAYA, NS
DOKLADY AKADEMII NAUK SSSR, 1973, 208 (06): : 1282 - 1285
[23] EFFECT OF FILTERS ON FSK WITH PIECEWISE-CONSTANT SHAPING FUNCTIONS.
Korn, I.
Electronics Letters, 1986, 22 (08) : 445 - 446
[24] A constructive enclosure approximation of a continuous function of many variables by piecewise linear functions
Okazaki, Hideaki
Nakano, Hideo
IEICE NONLINEAR THEORY AND ITS APPLICATIONS, 2016, 7 (02): : 295 - 311
[25] Solution of Optimal Control Problem in Class of Piecewise-Constant Functions
Aida-Zadeh, K. R.
Ragimov, A. B.
AUTOMATIC CONTROL AND COMPUTER SCIENCES, 2007, 41 (01) : 18 - 24
[26] Approximation of the Classes of Periodic Functions of One and Many Variables from the Nikol’skii–Besov and Sobolev Spaces
A. S. Romanyuk
S. Ya. Yanchenko
Ukrainian Mathematical Journal, 2022, 74 : 967 - 980
[27] APPROXIMATION OF CONTINUOUS PERIODIC-FUNCTIONS OF MANY VARIABLES BY THE FOURIER SUMS
GAVRILYUK, VT
DOPOVIDI AKADEMII NAUK UKRAINSKOI RSR SERIYA A-FIZIKO-MATEMATICHNI TA TECHNICHNI NAUKI, 1981, (02): : 8 - 10
[28] APPROXIMATION OF CONTINUOUS PERIODIC FUNCTIONS OF MANY VARIABLES BY RISS SPHERIC SUMS
STEPANET.OI
DOPOVIDI AKADEMII NAUK UKRAINSKOI RSR SERIYA A-FIZIKO-MATEMATICHNI TA TECHNICHNI NAUKI, 1974, (06): : 534 - 537
[29] On estimates of approximation characteristics of the Besov classes of periodic functions of many variables
A. S. Romanyuk
Ukrainian Mathematical Journal, 1997, 49 (9) : 1409 - 1422
[30] Approximation of the Classes HpΩ of Periodic Functions of Many Variables in the Space Lp
N. V. Derev’yanko
Ukrainian Mathematical Journal, 2014, 66 : 707 - 718

← 1 2 3 4 5 →