Geodesic
Connection between sets of uniqueness for multiplicative systems of functions and sets of uniqueness for multiplicative transforms
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2010), pp. 18-25

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A problem of uniqueness in the theory of series over multiplicative system of functions and in the theory of multiplicative transforms is considered. It is shown that every set of uniqueness for multiplicative transform is specified by a countable collection of sets of uniqueness for series over the corresponding multiplicative system of functions. Whereas every set of uniqueness for series over multiplicative system of functions is a portion on $[0,1)$ of some set of uniqueness for the corresponding multiplicative transform. 
@article{VMUMM_2010_1_a2,
     author = {T. A. Zherebyova},
     title = {Connection between sets of uniqueness for multiplicative systems of functions and sets of uniqueness for multiplicative transforms},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {18--25},
     publisher = {mathdoc},
     number = {1},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2010_1_a2/}
}
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T. A. Zherebyova. Connection between sets of uniqueness for multiplicative systems of functions and sets of uniqueness for multiplicative transforms. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2010), pp. 18-25. http://geodesic.mathdoc.fr/item/VMUMM_2010_1_a2/