Abstract:
The paper contains two main results. First we describe one-dimensional Franklin series converging everywhere
except possibly on a finite set to an everywhere-finite integrable function. Second we establish a class of subsets
of [0,1]2 with the following property. If a double Franklin series converges everywhere except on this set to an everywhere-finite integrable function, then it is the Fourier–Franklin series of this function. In particular, all countable
sets are in this class.
Keywords:
uniqueness theorem, U-set, Vallée–Poussin set, Franklin system, double series.
\Bibitem{Gev20}
\by G.~G.~Gevorkyan
\paper Uniqueness theorems for one-dimensional and double Franklin series
\jour Izv. Math.
\yr 2020
\vol 84
\issue 5
\pages 829--844
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\crossref{https://doi.org/10.1070/IM8889}
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Linking options:
https://www.mathnet.ru/eng/im8889
https://doi.org/10.1070/IM8889
https://www.mathnet.ru/eng/im/v84/i5/p3
This publication is cited in the following 4 articles:
Jiayi Zhu, Kang Huang, Yuanjie Xian, “General K-order Franklin wavelet method for numerical solution of integral equations”, Journal of Computational and Applied Mathematics, 2025, 116607
Jiayi Zhu, Kang Huang, Guohai Gao, Dongyang Yu, “Accurate and fast quaternion fractional-order Franklin moments for color image analysis”, Digital Signal Processing, 155 (2024), 104756
M. G. Plotnikov, “Uniqueness sets of positive measure for the trigonometric system”, Izv. Math., 86:6 (2022), 1179–1203
G. G. Gevorkyan, L. A. Akopyan, “Uniqueness Theorems for Multiple Franklin Series Converging over Rectangles”, Math. Notes, 109:2 (2021), 208–217
Citation in format AMSBIB
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