Geodesic
Uniqueness Questions for Some Classes of Haar Series
Matematičeskie zametki, Tome 75 (2004) no. 3, pp. 392-404 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

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