ON DIVERGENCE OF FOURIER–WALSH SERIES OF CONTINUOUS FUNCTION

S.A. Sargsyan

doi:10.46991/PYSU:A/2015.49.2.026

ON DIVERGENCE OF FOURIER–WALSH SERIES OF CONTINUOUS FUNCTION

Authors

S.A. Sargsyan Chair of Higher Mathematics, Faculty of Physics, YSU, Armenia

DOI:

https://doi.org/10.46991/PYSU:A/2015.49.2.026

Keywords:

Fourier–Walsh series, continuous function, divergence

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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Published

2015-06-12

How to Cite

Sargsyan, S. (2015). ON DIVERGENCE OF FOURIER–WALSH SERIES OF CONTINUOUS FUNCTION. Proceedings of the YSU A: Physical and Mathematical Sciences, 49(2 (237), 26–29. https://doi.org/10.46991/PYSU:A/2015.49.2.026