ON A UNIQUENESS THEOREM FOR THE FRANKLIN SYSTEM
DOI:
https://doi.org/10.46991/PYSU:A/2018.52.2.093Keywords:
majorant of partial sums, Franklin system, uniquenessAbstract
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 \text{mes} \{ x : \sup\limits_{n}{\left| S_{M_n} (x) \right|} > \lambda \} \to 0 $ as $ \lambda \to +\infty $. This shows that the boundedness assumption of the ratio $ \dfrac{ M_{n+1}}{M_n} $, used for the proofs of uniqueness theorems in earlier papers, can not be omitted.
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Published
2018-08-15
How to Cite
Navasardyan, K. (2018). ON A UNIQUENESS THEOREM FOR THE FRANKLIN SYSTEM. Proceedings of the YSU A: Physical and Mathematical Sciences, 52(2 (246), 93–100. https://doi.org/10.46991/PYSU:A/2018.52.2.093
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Mathematics
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