On multiple null-series in the Walsh system, M- and U- sets

2025/07/31 by Kazakova, A. D., Plotnikov, M. G.
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.00182

Abstract

A family of M-sets and null-series for the d-dimensional Walsh system is constructed if we consider convergence over rectangles, cubes, or iterated convergence. Non-empty portions of the constructed M-sets are also M-sets. The question of the rate of convergence to zero of the coefficients of zero-series that realize the constructed M-sets is studied, and it is shown how to modify the construction of the latter to turn them into U-sets

Citations

• On lacunarity and uniqueness for p-ary analogues of Rademacher chaos
• Cantor uniqueness and multiplicity along subsequences

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