Abstract:
Multiple Walsh series (S) on the group Gm 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:
dyadic group, multiple Walsh series, uniqueness sets, recovery problem for the coefficients of orthogonal series.
Citation:
M. G. Plotnikov, “Quasi-measures on the group Gm, Dirichlet sets, and uniqueness problems for multiple Walsh series”, Sb. Math., 201:12 (2010), 1837–1862
\Bibitem{Plo10}
\by M.~G.~Plotnikov
\paper Quasi-measures on the group $G^m$, Dirichlet sets, and uniqueness problems for multiple Walsh series
\jour Sb. Math.
\yr 2010
\vol 201
\issue 12
\pages 1837--1862
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Linking options:
https://www.mathnet.ru/eng/sm7625
https://doi.org/10.1070/SM2010v201n12ABEH004134
https://www.mathnet.ru/eng/sm/v201/i12/p131
This publication is cited in the following 5 articles:
S. F. Lukomskii, “On the Uniqueness Sets of Multiple Walsh Series for Convergence in Cubes”, Math. Notes, 109:3 (2021), 427–434
Plotnikov M., “V-Sets in the Products of Zero-Dimensional Compact Abelian Groups”, Eur. J. Math., 5:1, SI (2019), 223–240
Kholshchevnikova N., “The Union Problem and the Category Problem of Sets of Uniqueness in the Theory of Orthogonal Series”, Real Anal. Exch., 44:1 (2019), 65–76
M. G. Plotnikov, “λ-Convergence of Multiple Walsh–Paley Series and Sets of Uniqueness”, Math. Notes, 102:2 (2017), 268–276
M. G. Plotnikov, “Coefficients of convergent multiple Walsh-Paley series”, Sb. Math., 203:9 (2012), 1295–1309
Citation in format AMSBIB
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