Smoothness of functions and Fourier coefficients

M. I. Dyachenko; A. B. Mukanov; S. Yu Tikhonov

doi:10.1070/SM9096

Smoothness of functions and Fourier coefficients

M. I. Dyachenko, A. B. Mukanov, S. Yu Tikhonov

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1 Citation (Scopus)

Abstract

© 2019 Russian Academy of Sciences (DoM), London Mathematical Society, Turpion Ltd. We consider functions represented as trigonometric series with general monotone Fourier coefficients. The main result of the paper is the equivalence of the Lp modulus of smoothness, 1 < p < ∞, of such functions to certain sums of their Fourier coefficients. As applications, for such functions we give a description of the norm in the Besov space and sharp direct and inverse theorems in approximation theory.

Original language	English
Pages (from-to)	994-1018
Number of pages	25
Journal	Sbornik Mathematics
Volume	210
Issue number	7
DOIs	https://doi.org/10.1070/SM9096
Publication status	Published - Jul 2019

Keywords

CONTINUITY
Fourier series
L-P
MODULI
MONOTONICITY
TRANSFORMS
TRIGONOMETRIC SERIES
general monotone sequences
moduli of smoothness

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http://www.mendeley.com/research/smoothness-functions-fourier-coefficients

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title = "Smoothness of functions and Fourier coefficients",

abstract = "{\textcopyright} 2019 Russian Academy of Sciences (DoM), London Mathematical Society, Turpion Ltd. We consider functions represented as trigonometric series with general monotone Fourier coefficients. The main result of the paper is the equivalence of the Lp modulus of smoothness, 1 < p < ∞, of such functions to certain sums of their Fourier coefficients. As applications, for such functions we give a description of the norm in the Besov space and sharp direct and inverse theorems in approximation theory.",

keywords = "CONTINUITY, Fourier series, L-P, MODULI, MONOTONICITY, TRANSFORMS, TRIGONOMETRIC SERIES, general monotone sequences, moduli of smoothness",

author = "Dyachenko, {M. I.} and Mukanov, {A. B.} and Tikhonov, {S. Yu}",

year = "2019",

month = jul,

doi = "10.1070/SM9096",

language = "English",

volume = "210",

pages = "994--1018",

journal = "Sbornik Mathematics",

issn = "1064-5616",

publisher = "Turpion Ltd.",

number = "7",

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TY - JOUR

T1 - Smoothness of functions and Fourier coefficients

AU - Dyachenko, M. I.

AU - Mukanov, A. B.

AU - Tikhonov, S. Yu

PY - 2019/7

Y1 - 2019/7

N2 - © 2019 Russian Academy of Sciences (DoM), London Mathematical Society, Turpion Ltd. We consider functions represented as trigonometric series with general monotone Fourier coefficients. The main result of the paper is the equivalence of the Lp modulus of smoothness, 1 < p < ∞, of such functions to certain sums of their Fourier coefficients. As applications, for such functions we give a description of the norm in the Besov space and sharp direct and inverse theorems in approximation theory.

AB - © 2019 Russian Academy of Sciences (DoM), London Mathematical Society, Turpion Ltd. We consider functions represented as trigonometric series with general monotone Fourier coefficients. The main result of the paper is the equivalence of the Lp modulus of smoothness, 1 < p < ∞, of such functions to certain sums of their Fourier coefficients. As applications, for such functions we give a description of the norm in the Besov space and sharp direct and inverse theorems in approximation theory.

KW - CONTINUITY

KW - Fourier series

KW - L-P

KW - MODULI

KW - MONOTONICITY

KW - TRANSFORMS

KW - TRIGONOMETRIC SERIES

KW - general monotone sequences

KW - moduli of smoothness

UR - http://www.mendeley.com/research/smoothness-functions-fourier-coefficients

U2 - 10.1070/SM9096

DO - 10.1070/SM9096

M3 - Article

VL - 210

SP - 994

EP - 1018

JO - Sbornik Mathematics

JF - Sbornik Mathematics

SN - 1064-5616

IS - 7

ER -