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 Proceedings of the YSU, Physics & Mathematics, 2018, Volume 52, Issue 2, Pages 93–100 (Mi uzeru464)

Mathematics

On a uniqueness theorem for the Franklin system

K. A. Navasardyan

Chair of Numerical Analysis and Mathematical Modelling YSU, Armenia

Abstract: In this paper we prove that there exist a nontrivial Franklin series and a sequence$M_n$ such that the partial sums$S_{M_n}(x)$ of that series converge to 0 almost everywhere and $\lambda\cdot \mathrm{mes}\{x:sup_n|S_{M_n}(x)|>\lambda\}\to 0$ as $\lambda\to+\infty$. This shows that the boundedness assumption of the ratio $M_{n+1} /M_n$, used for the proofs of uniqueness theorems in earlier papers, can not be omitted.

Keywords: majorant of partial sums, Franklin system, uniqueness.

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Document Type: Article
MSC: 42C10
Revised: 20.04.2018
Language: English

Citation: K. A. Navasardyan, “On a uniqueness theorem for the Franklin system”, Proceedings of the YSU, Physics & Mathematics, 52:2 (2018), 93–100

Citation in format AMSBIB
\Bibitem{Nav18} \by K.~A.~Navasardyan \paper On a uniqueness theorem for the Franklin system \jour Proceedings of the YSU, Physics {\&} Mathematics \yr 2018 \vol 52 \issue 2 \pages 93--100 \mathnet{http://mi.mathnet.ru/uzeru464}