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Quasi-measures on the group $G^m$, Dirichlet sets, and uniqueness problems for multiple Walsh series
Sbornik. Mathematics, Tome 201 (2010) no. 12, pp. 1837-1862 Cet article a éte moissonné depuis la source Math-Net.Ru

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Multiple Walsh series $(S)$ on the group $G^m$ are studied. It is proved that every at most countable set is a uniqueness set for series $(S)$ under convergence over cubes. The recovery problem is solved for the coefficients of series $(S)$ that converge outside countable sets or outside sets of Dirichlet type. A number of analogues of the de la Vallée Poussin theorem are established for series $(S)$. Bibliography: 28 titles.
Keywords: multiple Walsh series, uniqueness sets, recovery problem for the coefficients of orthogonal series.
Mots-clés : dyadic group 
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M. G. Plotnikov. Quasi-measures on the group $G^m$, Dirichlet sets, and uniqueness problems for multiple Walsh series. Sbornik. Mathematics, Tome 201 (2010) no. 12, pp. 1837-1862. http://geodesic.mathdoc.fr/item/SM_2010_201_12_a6/

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