Natural Sciences, Mathematics, 2026
ON FOURIER COEFFICIENTS WITH RESPECT TO THE WALSH DOUBLE SYSTEM
This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution,
and reproduction in any medium, provided the original work is properly cited.
Submitted: 2025-02-17
© 2026 by author(s) and The Gufo Inc.
This work is licensed under Creative Commons Attribution–NonCommercial International License
(CC BY-NC 4.0).
Abstract
In the present paper we will consider the behavior of Fourier coefficients with respect to the Walsh double system after modification of functions. We prove that for any function f(x,y)∈Lp[0,1]2 one can find a function g∈Lp[0,1]2 coinciding with f(x,y) on a small measure such that the non-zero coefficients of g(x,y) are monotonically decreasing over all rays by absolute values.