On the divergence of subsequences of partial Walsh-Fourier sums

Ushangi Goginava; Giorgi Oniani

doi:10.1016/j.jmaa.2020.124900

On the divergence of subsequences of partial Walsh-Fourier sums

Ushangi Goginava
, Giorgi Oniani

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

A class of increasing sequences of natural numbers (n_k) is found for which there exists a function f∈L[0,1) such that the subsequence of partial Walsh-Fourier sums (S_{n_k}(f)) diverges everywhere. A condition for the growth order of a function φ:[0,∞)→[0,∞) is given fulfillment of which implies an existence of above type function f in the class φ(L)[0,1).

Original language	English
Article number	124900
Journal	Journal of Mathematical Analysis and Applications
Volume	497
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2020.124900
Publication status	Published - May 15 2021

Keywords

Everywhere divergence
Subsequence of partial sums
Walsh-Fourier series

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2020.124900

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abstract = "A class of increasing sequences of natural numbers (nk) is found for which there exists a function f∈L[0,1) such that the subsequence of partial Walsh-Fourier sums (Snk(f)) diverges everywhere. A condition for the growth order of a function φ:[0,∞)→[0,∞) is given fulfillment of which implies an existence of above type function f in the class φ(L)[0,1).",

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AU - Oniani, Giorgi

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AB - A class of increasing sequences of natural numbers (nk) is found for which there exists a function f∈L[0,1) such that the subsequence of partial Walsh-Fourier sums (Snk(f)) diverges everywhere. A condition for the growth order of a function φ:[0,∞)→[0,∞) is given fulfillment of which implies an existence of above type function f in the class φ(L)[0,1).

KW - Everywhere divergence

KW - Subsequence of partial sums

KW - Walsh-Fourier series

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On the divergence of subsequences of partial Walsh-Fourier sums

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Keywords

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