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Trigonometric series and the permutation sign convergence condition

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Abstract

We prove that a uniformly convergent trigonometric series may not satisfy the permutation sign convergence condition, hence it may not satisfy the Rademacher condition as well.

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Acknowledgements

The authors are grateful to Professor S. Kwapien (Poland); the intensive discussion with him led us to the proof of Theorem 1.11 given above. We also are grateful to referees for remarks and suggestions. Our special thanks goes to the fourth referee, whose remarks related with Conjecture 1.4 obliged us to read more carefully [22] and to discover the articles [6,9,12-14].

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Authors and Affiliations

  1. Muskhelishvili Institute of Computational Mathematics of the Georgian Technical University, 0159, Tbilisi, Georgia

    G. Chelidze, S. Chobanyan, G. Giorgobiani & V. Tarieladze

  2. Kutaisi International University, 4600, Kutaisi, Georgia

    G. Chelidze

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  1. G. Chelidze
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  2. S. Chobanyan
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  3. G. Giorgobiani
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  4. V. Tarieladze
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Correspondence to G. Giorgobiani.

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The third author was supported by the European Commission’s HORIZON EUROPE Grant Project GAIN.

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Chelidze, G., Chobanyan, S., Giorgobiani, G. et al. Trigonometric series and the permutation sign convergence condition. Anal Math 50, 101–110 (2024). https://doi.org/10.1007/s10476-024-00012-1

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  • DOI: https://doi.org/10.1007/s10476-024-00012-1

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