2018; Physical and Mathematical Sciences, 52(2 (246): 93–100
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ON A UNIQUENESS THEOREM FOR THE FRANKLIN SYSTEM

K Navasard*

Received: 2025-02-04 · Published: 2018-08-15

© 2018 The Author(s) and the original publisher.

CC BY-NC 4.0 This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
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Original title
ON A UNIQUENESS THEOREM FOR THE FRANKLIN SYSTEM
Author
K Navasard
Published
2018-08-15
Licence
Creative Commons Attribution-NonCommercial 4.0 International
Original
https://doi.org/10.46991/PYSU:A/2018.52.2.093

Abstract

In this paper we prove that there exist a nontrivial Franklin series and asequenceMnsuch that the partial sumsSMn(x)of that series converge to 0almost everywhere andλ·mes{x: supn|SMn(x)|>λ}→0 asλ→+∞.Thisshows that the boundedness assumption of the ratioMn+1Mn, used for the proofsof uniqueness theorems in earlier papers, can not be omitted
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