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On Convergence of Partial Sums of Franklin Series to +∞

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Abstract

In this paper, we prove that if {nk} is an arbitrary increasing sequence of natural numbers such that the ratio nk+1/nk is bounded, then the nk-th partial sum of a series by Franklin system cannot converge to +∞ on a set of positive measure. Also, we prove that if the ratio nk+1/nk is unbounded, then there exists a series by Franklin system, the nk-th partial sum of which converges to +∞ almost everywhere on [0, 1].

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Authors and Affiliations

  1. Yerevan State University, Yerevan, Armenia

    K. A. Navasardyan & V. G. Mikayelyan

Authors
  1. K. A. Navasardyan
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  2. V. G. Mikayelyan
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Corresponding authors

Correspondence to K. A. Navasardyan or V. G. Mikayelyan.

Additional information

Russian Text © The Author(s), 2019, published in Izvestiya Natsional’noi Akademii Nauk Armenii, Matematika, 2019, No. 6, pp. 54–65.

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Navasardyan, K.A., Mikayelyan, V.G. On Convergence of Partial Sums of Franklin Series to +∞. J. Contemp. Mathemat. Anal. 54, 347–354 (2019). https://doi.org/10.3103/S1068362319060049

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  • DOI: https://doi.org/10.3103/S1068362319060049

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