Geodesic
Multiple Walsh Series and Zygmund Sets
Matematičeskie zametki, Tome 95 (2014) no. 5, pp. 750-762

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The classical Zygmund theorem claims that, for any sequence of positive numbers $\{\varepsilon_n\}$ monotonically tending to zero and any $\delta>0$, there exists a set of uniqueness for the class of trigonometric series whose coefficients are majorized by the sequence $\{\varepsilon_n\}$ whose measure is greater than $2\pi-\delta$. In this paper, we prove the analog of Zygmund's theorem for multiple series in the Walsh system on whose coefficients rather weak constraints are imposed.
Keywords: multiple Walsh series, Zygmund set, set of uniqueness, binary group, Abelian group, binary cube, quasimeasure. 
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     author = {M. G. Plotnikov},
     title = {Multiple {Walsh} {Series} and {Zygmund} {Sets}},
     journal = {Matemati\v{c}eskie zametki},
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     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2014_95_5_a9/}
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M. G. Plotnikov. Multiple Walsh Series and Zygmund Sets. Matematičeskie zametki, Tome 95 (2014) no. 5, pp. 750-762. http://geodesic.mathdoc.fr/item/MZM_2014_95_5_a9/