Geodesic
On uniqueness for Franklin series with a~convergent subsequence of partial sums
Sbornik. Mathematics, Tome 214 (2023) no. 2, pp. 197-209

Voir la notice de l'article provenant de la source Math-Net.Ru

We show that if the partial sums $S_{n_i}(x)=\sum_{k=0}^{n_i}a_kf_k(x)$ of a Franklin series $\sum_{k=0}^{\infty}a_kf_k(x)$, where $\sup_i{n_i}/(n_{i-1})\infty$, converge in measure to a bounded function $f$ and $\sup_i|S_{n_i}(x)|\infty$ for $ x\not\in B$, where $B$ is some countable set, then this series is the Fourier-Franklin series of $f$. Bibliography: 24 titles.
Keywords: Franklin system, Franklin series, uniqueness theorem, Fourier-Franklin series. 
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     author = {G. G. Gevorkyan},
     title = {On uniqueness for {Franklin} series with a~convergent subsequence of partial sums},
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G. G. Gevorkyan. On uniqueness for Franklin series with a~convergent subsequence of partial sums. Sbornik. Mathematics, Tome 214 (2023) no. 2, pp. 197-209. http://geodesic.mathdoc.fr/item/SM_2023_214_2_a2/