Geodesic
Uniqueness Questions for Some Classes of Haar Series
Matematičeskie zametki, Tome 75 (2004) no. 3, pp. 392-404

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Sets of relative uniqueness for Haar series are studied. Whole classes of conditions on the behavior of a Haar series, including the Arutyunyan–Talalyan condition, are considered. New numerical characteristic of perfect sets are introduced. They are used to obtain necessary conditions and sufficient conditions for a given set to be a set of relative uniqueness under certain assumptions. Thereby, the 1967 results of G. M. Mushegyan are generalized. Moreover, for $0$, the existence of perfect $\operatorname{U}$-sets with the $\operatorname{G}(p)$-conditions introduced by W. Wade in 1981 is proved and a method for constructing such sets is given. 
@article{MZM_2004_75_3_a6,
     author = {M. G. Plotnikov},
     title = {Uniqueness {Questions} for {Some} {Classes} of {Haar} {Series}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {392--404},
     publisher = {mathdoc},
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     number = {3},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2004_75_3_a6/}
}
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M. G. Plotnikov. Uniqueness Questions for Some Classes of Haar Series. Matematičeskie zametki, Tome 75 (2004) no. 3, pp. 392-404. http://geodesic.mathdoc.fr/item/MZM_2004_75_3_a6/