On multiple null-series in the Walsh system, M- and U- sets
Classical Analysis and ODEs
2025-12-23 v2
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
Cite
@article{arxiv.2508.00182,
title = {On multiple null-series in the Walsh system, M- and U- sets},
author = {A. D. Kazakova and M. G. Plotnikov},
journal= {arXiv preprint arXiv:2508.00182},
year = {2025}
}
Comments
25 pages, in Russian language. 1 figures