Geodesic
On Uniqueness Sets for Multiple Walsh Series
Matematičeskie zametki, Tome 81 (2007) no. 2, pp. 265-279

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We study uniqueness sets for multiple Walsh series under $\rho$-regular (or bounded) convergence in rectangles. We prove that a countable set is a uniqueness set for such a series under this convergence. We construct a class of perfect uniqueness sets for multiple Walsh series under this convergence. We show that the notion of index of a perfect set does not solve the problem of whether this set belongs to the class of uniqueness sets. We note that the results of this paper remain valid for several rearranged multiple Walsh series.
Keywords: multiple Walsh series, $\rho$-regular convergence, uniqueness set ($U$-set), $M$-set, perfect set, Rademacher function. 
@article{MZM_2007_81_2_a9,
     author = {M. G. Plotnikov},
     title = {On {Uniqueness} {Sets} for {Multiple} {Walsh} {Series}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {265--279},
     publisher = {mathdoc},
     volume = {81},
     number = {2},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_81_2_a9/}
}
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M. G. Plotnikov. On Uniqueness Sets for Multiple Walsh Series. Matematičeskie zametki, Tome 81 (2007) no. 2, pp. 265-279. http://geodesic.mathdoc.fr/item/MZM_2007_81_2_a9/