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<p>The Fourier–Walsh series of even continuous functions may be divergent at some points. Moreover, among integrable functions, there are functions such that their Fourier–Walsh series diverge everywhere on [0, 1). In this connection, it becomes necessary to consider various summation methods allowing one to restore a function according to its Fourier–Walsh series. We also study the Besov space on a dyadic group in terms of the strong summability. Finally, we present necessary information about the Fourier– Walsh transform.</p>

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On the Strong Summability of Fourier–Walsh Series in the Besov Space

  • 期刊论文

  • 发表日期：

    2025年2月1日

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  • A. Igenberlina,
  • Zh. Keulimzhayeva

摘要

The Fourier–Walsh series of even continuous functions may be divergent at some points. Moreover, among integrable functions, there are functions such that their Fourier–Walsh series diverge everywhere on [0, 1). In this connection, it becomes necessary to consider various summation methods allowing one to restore a function according to its Fourier–Walsh series. We also study the Besov space on a dyadic group in terms of the strong summability. Finally, we present necessary information about the Fourier– Walsh transform.