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Uniqueness Theorems for Multiple Franklin Series Converging over Rectangles

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Abstract

It is proved that if a multiple series in the Franklin system converges in the sense of Pringsheim everywhere, except, perhaps, on a set that is a Cartesian product of sets of measure zero, to an everywhere finite integrable function, then it is the Fourier–Franklin series of this function. A uniqueness theorem is also proved for multiple Franklin series whose rectangular partial sums at each point have a sequential limit.

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Funding

This work was supported by the State Committee on Science of the Republic of Armenia (grant no. 18T-1A074).

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Authors and Affiliations

  1. Yerevan State University, 375025, Yerevan, Armenia

    G. G. Gevorkyan & L. A. Hakobyan

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  1. G. G. Gevorkyan
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  2. L. A. Hakobyan
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Correspondence to G. G. Gevorkyan.

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Gevorkyan, G.G., Hakobyan, L.A. Uniqueness Theorems for Multiple Franklin Series Converging over Rectangles. Math Notes 109, 208–217 (2021). https://doi.org/10.1134/S0001434621010247

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  • DOI: https://doi.org/10.1134/S0001434621010247

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