Geodesic
Uniqueness theorems for Franklin series
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Harmonic analysis, approximation theory, and number theory, Tome 303 (2018), pp. 67-86

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Simple Franklin series are investigated that converge to zero everywhere except for one point (or several points). It is also proved that the one-point set (or a finite set) is a uniqueness set for Pringsheim convergent double series. 
@article{TM_2018_303_a6,
     author = {G. G. Gevorkyan},
     title = {Uniqueness theorems for {Franklin} series},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {67--86},
     publisher = {mathdoc},
     volume = {303},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2018_303_a6/}
}
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G. G. Gevorkyan. Uniqueness theorems for Franklin series. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Harmonic analysis, approximation theory, and number theory, Tome 303 (2018), pp. 67-86. http://geodesic.mathdoc.fr/item/TM_2018_303_a6/