Quasi-measures on the group $G^m$, Dirichlet sets, and uniqueness problems for multiple Walsh series

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.