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Series Formed by the Moduli of Blocks of Terms of Trigonometric Series. A Survey

Abstract

This paper presents a survey of results on properties of series composed of the moduli of blocks of trigonometric series. The following questions are addressed: convergence, uniform convergence, and membership of the sum of series to L p and to weighted L p spaces. First results in this area pertaining to similar series for the Walsh system are put forward.

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Correspondence to S. A. Telyakovskii.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 18, No. 5, pp. 209–216, 2013.

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Telyakovskii, S.A. Series Formed by the Moduli of Blocks of Terms of Trigonometric Series. A Survey. J Math Sci 209, 152–158 (2015). https://doi.org/10.1007/s10958-015-2492-4

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Keywords

  • Fourier Series
  • Uniform Convergence
  • Bounded Variation
  • Trigonometric Series
  • Absolute Constant