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<p>The existence is proved of a sequence of natural numbers of zero density with the following property:If the subsequence of partial sums of a Haar series with indices from this sequence converges everywhere to an everywhere finite function integrable in the sense of Perron, then the given series is the Fourier–Haar series of its sum.</p>

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On Recovering the Coefficients of a Haar Series Convergent Along a Subsequence of Partial Sums

  • 期刊论文

  • 发表日期：

    2026年3月28日

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  • G. G. Gevorkyan,
  • V. A. Skvortsov

摘要

The existence is proved of a sequence of natural numbers of zero density with the following property:If the subsequence of partial sums of a Haar series with indices from this sequence converges everywhere to an everywhere finite function integrable in the sense of Perron, then the given series is the Fourier–Haar series of its sum.