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<p>It is a well known result that a trigonometric series cannot tend to <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(+\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>+</mo> <mi>∞</mi> </mrow> </math></EquationSource> </InlineEquation> on a set of a positive measure. Recently, the authors proved that a similar result holds also for 1D Ciesielski series. In this paper we extend this result to multivariate case, and obtain a criterion for divergence to <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(+\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>+</mo> <mi>∞</mi> </mrow> </math></EquationSource> </InlineEquation> for cubic partial sums of a multiple Ciesielski series.</p>

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Criterion for Divergence to \(+\infty \) for Multiple Ciesielski Series

  • 期刊论文

  • 发表日期：

    2026年1月12日

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  • Gegham G. Gevorkyan,
  • Karen A. Keryan,
  • Michael P. Poghosyan

摘要

It is a well known result that a trigonometric series cannot tend to \(+\infty \) + ∞ on a set of a positive measure. Recently, the authors proved that a similar result holds also for 1D Ciesielski series. In this paper we extend this result to multivariate case, and obtain a criterion for divergence to \(+\infty \) + ∞ for cubic partial sums of a multiple Ciesielski series.