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<p>We establish a direct estimate for the approximation rate of the iterated Boolean sums of the generalized sampling operator in the uniform norm on the real line. We complement that estimate with a strong converse inequality, which shows that it is best possible. Our approach relies on results about the simultaneous approximation by the generalized sampling operator.</p>

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Approximation by iterated Boolean sums of sampling operators

  • 期刊论文

  • 发表日期：

    2026年7月8日

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  • Tuncer Acar,
  • Borislav R. Draganov,
  • Metin Turgay

摘要

We establish a direct estimate for the approximation rate of the iterated Boolean sums of the generalized sampling operator in the uniform norm on the real line. We complement that estimate with a strong converse inequality, which shows that it is best possible. Our approach relies on results about the simultaneous approximation by the generalized sampling operator.