Geodesic
Uniqueness theorems for one-dimensional and double Franklin series
Izvestiya. Mathematics , Tome 84 (2020) no. 5, pp. 829-844

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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, Franklin system, double series.
Mots-clés : Vallée–Poussin set 
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     author = {G. G. Gevorkyan},
     title = {Uniqueness theorems for one-dimensional and double {Franklin} series},
     journal = {Izvestiya. Mathematics },
     pages = {829--844},
     publisher = {mathdoc},
     volume = {84},
     number = {5},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2020_84_5_a0/}
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G. G. Gevorkyan. Uniqueness theorems for one-dimensional and double Franklin series. Izvestiya. Mathematics , Tome 84 (2020) no. 5, pp. 829-844. http://geodesic.mathdoc.fr/item/IM2_2020_84_5_a0/