Geodesic
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

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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 
@article{SM_2010_201_12_a6,
     author = {M. G. Plotnikov},
     title = {Quasi-measures on the group $G^m$, {Dirichlet} sets, and uniqueness problems for multiple {Walsh} series},
     journal = {Sbornik. Mathematics},
     pages = {1837--1862},
     publisher = {mathdoc},
     volume = {201},
     number = {12},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2010_201_12_a6/}
}
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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/