Estimate for the Rate of Uniform Convergence of the Fourier Series of a Continuous Periodic Function of Bounded $$p$$ -Variation

IF 0.6 4区数学 Q3 MATHEMATICS

Mathematical Notes Pub Date : 2024-04-22 DOI:10.1134/s0001434624010243

T. Yu. Semenova

引用次数: 0

Abstract

We obtain an estimate for the convergence rate of the Fourier series of a continuous periodic function in terms of the modulus of continuity of the function and the value of its $p$-variation. We prove that the leading term of the estimate is sharp.

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有界 $$p$$ 变量的连续周期函数的傅里叶级数均匀收敛率估计

摘要我们根据连续周期函数的连续性模量及其 $p$- 变量的值，得到了连续周期函数傅里叶级数收敛率的估计值。我们证明了该估计的前导项是尖锐的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Notes 数学-数学

CiteScore

0.90

自引率

16.70%

发文量

179

审稿时长

24 months

期刊介绍： Mathematical Notes is a journal that publishes research papers and review articles in modern algebra, geometry and number theory, functional analysis, logic, set and measure theory, topology, probability and stochastics, differential and noncommutative geometry, operator and group theory, asymptotic and approximation methods, mathematical finance, linear and nonlinear equations, ergodic and spectral theory, operator algebras, and other related theoretical fields. It also presents rigorous results in mathematical physics.