Geodesic
On uniqueness for series in the general Franklin system
Sbornik. Mathematics, Tome 215 (2024) no. 3, pp. 308-322

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We prove some uniqueness theorems for series in general Franklin systems. In particular, for series in the classical Franklin system our result asserts that if the partial sums $S_{n_i}(x)=\sum_{k=0}^{n_i}a_kf_k(x)$ of a Franklin series $\sum_{k=0}^{\infty}a_kf_k(x)$ converge in measure to an integrable function $f$ and $\sup_i|S_{n_i}(x)|\infty$, for $x\notin B$, where $B$ is some countable set and $\sup_i(n_i/n_{i-1})\infty$, then this is the Fourier–Franklin series of $f$. Bibliography: 29 titles.
Keywords: Franklin system, Franklin series, general Franklin system, uniqueness theorem, Fourier–Franklin series. 
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     author = {G. G. Gevorkyan},
     title = {On uniqueness for series in the general {Franklin} system},
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G. G. Gevorkyan. On uniqueness for series in the general Franklin system. Sbornik. Mathematics, Tome 215 (2024) no. 3, pp. 308-322. http://geodesic.mathdoc.fr/item/SM_2024_215_3_a1/