On Universal Fourier Series in the Walsh System

We prove some theorems concerning the existence of functions whose Fourier series in the Walsh system are universal in the class of all measurable functions in the sense of signs in the cases of convergence in measure and almost everywhere convergence.

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Bibliographic Details
Published in:Siberian mathematical journal 2022-09, Vol.63 (5), p.868-882
Main Author: Grigoryan, M. G.
Format: Article
Language:English
Subjects:
Convergence
Existence theorems
Fourier series
Mathematics
Mathematics and Statistics
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Description
Summary:We prove some theorems concerning the existence of functions whose Fourier series in the Walsh system are universal in the class of all measurable functions in the sense of signs in the cases of convergence in measure and almost everywhere convergence.
ISSN:0037-4466
1573-9260
DOI:10.1134/S0037446622050068