Geodesic
On the uniqueness of series with respect to characters of dyadic groups
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 9 (2009) no. 2, pp. 38-44

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Conditions on series with respect to characters of dyadic groups are specified by which finite or countable set is the set of uniqueness. 
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     author = {N. S. Polyakova},
     title = {On the uniqueness of series with respect to characters of dyadic groups},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
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N. S. Polyakova. On the uniqueness of series with respect to characters of dyadic groups. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 9 (2009) no. 2, pp. 38-44. http://geodesic.mathdoc.fr/item/ISU_2009_9_2_a6/