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Unconditional Convergence of Fourier Series for Functions of Bounded Variation

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Abstract

This article concerns the unconditional convergence a.e. of Fourier series with respect to general orthonormal systems. We find certain conditions to be satisfied by the functions in the orthonormal system so that the Fourier series of each function of finite variation unconditionally converge a.e. The results are best possible.

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Authors and Affiliations

  1. Tbilisi State University, Tbilisi, Georgia

    L. D. Gogoladze & V. Sh. Tsagareishvili

Authors
  1. L. D. Gogoladze
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  2. V. Sh. Tsagareishvili
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Correspondence to L. D. Gogoladze.

Additional information

Original Russian Text Copyright © 2018 Gogoladze L.D. and Tsagareishvili V.Sh.

Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 59, No. 1, pp. 86–94, January–February, 2018; DOI: 10.17377/smzh.2018.59.108

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Gogoladze, L.D., Tsagareishvili, V.S. Unconditional Convergence of Fourier Series for Functions of Bounded Variation. Sib Math J 59, 65–72 (2018). https://doi.org/10.1134/S0037446618010081

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  • DOI: https://doi.org/10.1134/S0037446618010081

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