Multilayer Anisotropic Thin Film with a Twist
ISSN: 1829-1171
Submitted: 2026-07-17
Natural Sciences, Physics, 2026
ON THE ALMOST EVERYWHERE CONVERGENCE OF NEGATIVE ORDER CESARO MEANS OF FOURIER–WALSH SERIES
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: 2025-02-11
© 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 paper is presented existence of an increasing sequence of natural numbers Mν,ν=0,1,…, such that for any ε>0 there exists a measurable set E with a measure μE>1−ε, such that for any function f∈L1[0,1] one can find a function g∈L1[0,1], which coincides with the function f on E, and for any α≠−1,−2,… the Cesaro means σMνα(x,f~), ν=0,1,…, converges to g(x) almost everywhere on [0,1].