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Proceedings of the Yerevan State University, series Physical and Mathematical Sciences, 2018, Volume 52, Issue 2, Pages 93–100
(Mi uzeru464)
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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 $\lambda\cdot \mathrm{mes}\left\{x:sup_n\big|S_{M_n}(x)\big|>\lambda\right\}\to 0$ 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.
Received: 22.02.2018 Revised: 20.04.2018
Citation:
K. A. Navasardyan, “On a uniqueness theorem for the Franklin system”, Proceedings of the YSU, Physical and Mathematical Sciences, 52:2 (2018), 93–100
Linking options:
https://www.mathnet.ru/eng/uzeru464 https://www.mathnet.ru/eng/uzeru/v52/i2/p93
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Abstract page: | 110 | Full-text PDF : | 33 | References: | 15 |
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