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Abstract <p> H. Lebesgue’s classical estimate of the rate of convergence of Fourier sums of a continuous <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(2\pi\)</EquationSource> </InlineEquation>-periodic function in terms of its modulus of continuity is well known. In the present paper, this estimate is sharpened for continuous functions with constraints on the fractality of their graphs. The result is stated in terms of the modulus of continuity and a new characteristic of functions introduced in the paper, which is called the modulus of fractality. We prove that the estimate obtained cannot be sharpened in order. </p>

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Rate of Convergence of Fourier Sums of Continuous Functions with Fractal Graphs

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • N. Yu. Antonov,
  • M. L. Gridnev

摘要

Abstract

H. Lebesgue’s classical estimate of the rate of convergence of Fourier sums of a continuous \(2\pi\) -periodic function in terms of its modulus of continuity is well known. In the present paper, this estimate is sharpened for continuous functions with constraints on the fractality of their graphs. The result is stated in terms of the modulus of continuity and a new characteristic of functions introduced in the paper, which is called the modulus of fractality. We prove that the estimate obtained cannot be sharpened in order.