2015; Physical and Mathematical Sciences, 49(2 (237): 26–29
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ON DIVERGENCE OF FOURIER–WALSH SERIES OF CONTINUOUS FUNCTION

Stepan Sargsyan*

Received: 2025-02-11 · Published: 2015-06-12

© 2015 The Author(s) and the original publisher.

CC BY 4.0 This work is licensed under a Creative Commons Attribution 4.0 International License.
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Original title
ON DIVERGENCE OF FOURIER–WALSH SERIES OF CONTINUOUS FUNCTION
Author
Stepan Sargsyan
Published
2015-06-12
Licence
Creative Commons Attribution 4.0 International
Original
https://doi.org/10.46991/PYSUA.2015.49.2.026

Abstract

We prove that for any perfect set P of positive measure, for which 0 is a density point, one can construct a function f (x) continuous on [0, 1) such that each measurable and bounded function, which coincides with f (x) on the set P has diverging Fourier–Walsh series at 0.
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