On the strong summability of the Fourier–Walsh series in the Besov space

A. Igenberlina; Zh. Keulimzhayeva

doi:10.3842/umzh.v76i9.7577

A. Igenberlina L. N. Gumilyov Eurasian National University, Astana, Kazakhstan
Zh. Keulimzhayeva S. Seifullin Kazakh Agrotechnical University, Astana, Kazakhstan

DOI: https://doi.org/10.3842/umzh.v76i9.7577

Keywords: Walsh functions, dyadic group, Fourier transform, Besov space

Abstract

UDC 517.5

The Fourier–Walsh series of even continuous functions may be divergent at some points. Moreover, among integrable functions, there are functions such that their Fourier–Walsh series diverge everywhere on $[0,1)$. In this connection, it becomes necessary to consider various summation methods that would allow us to restore the function according to its Fourier–Walsh series. We also investigate the Besov space on a dyadic group in terms of strong summability. Finally, we present necessary information about the Fourier–Walsh transform.

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