On the divergence of subsequences of partial Walsh-Fourier sums

Ushangi Goginava; Giorgi Oniani

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arXiv · 1912.04808

On the divergence of subsequences of partial Walsh-Fourier sums

Ushangi Goginava·Giorgi Oniani

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Abstract

A class of increasing sequences of natural numbers $(n_k)$ is found for which there exists a function $f\in L[0,1)$ such that the subsequence of partial Walsh-Fourier sums $(S_{n_k}(f))$ diverge everywhere. A condition for the growth order of a function $\varphi:[0,\infty)\rightarrow[0,\infty)$ is given fulfilment of which implies an existence of above type function $f$ in the class $\varphi(L)[0,1)$.

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Ushangi Goginava, Giorgi Oniani. 2019-12-10. On the divergence of subsequences of partial Walsh-Fourier sums. https://arxiv.org/abs/1912.04808

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