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A Uniqueness Theorem for Franklin Series

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Abstract

In this paper we obtain, that if the partial sums \(\sigma_{q_{k}}(x)\) of a Franklin series converge in measure to a function \(f\), the ratio \(\frac{q_{k+1}}{q_{k}}\) is bounded and the majorant of partial sums satisfies to a necessary condition, then the coefficients of the series are restored by the function \(f\).

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Authors and Affiliations

  1. Yerevan State University, Yerevan, Armenia

    K. Keryan & A. Khachatryan

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  1. K. Keryan
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  2. A. Khachatryan
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Correspondence to K. Keryan.

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Keryan, K., Khachatryan, A. A Uniqueness Theorem for Franklin Series. J. Contemp. Mathemat. Anal. 55, 166–178 (2020). https://doi.org/10.3103/S106836232003005X

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  • DOI: https://doi.org/10.3103/S106836232003005X

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