ON THE ALMOST EVERYWHERE CONVERGENCE OF NEGATIVE ORDER CESARO MEANS OF FOURIER–WALSH SERIES

Authors

  • L.N. Galoyan Chair of Higher Mathematics of Radiophysics Faculty, YSU, Armenia
  • R.G. Melibekyan Chair of Higher Mathematics of Radiophysics Faculty, YSU, Armenia

DOI:

https://doi.org/10.46991/PSYU:A/2016.50.1.064

Keywords:

Fourier–Walsh series, Cesaro means

Abstract

In the paper is presented existence of an increasing sequence of natural numbers $M_{\nu}, \nu=0,1,... ,$ such that for any $\varepsilon>0$ there exists a measurable set $E$ with a measure $\mu E>1-\varepsilon,$ such that for any function $f\in L^{1}[0,1]$ one can find a function $g\in L^{1}[0,1],$ which coincides with the function $f$ on $E$, and for any $\alpha \neq-1,-2,...$ the Cesaro means $\sigma_{M_{\nu}}^{\alpha}(x,\tilde{f}),~\nu=0,1,...,$ converges to $g(x)$ almost everywhere on [0,1].

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Published

2016-03-18

How to Cite

Galoyan, L., & Melibekyan, R. (2016). ON THE ALMOST EVERYWHERE CONVERGENCE OF NEGATIVE ORDER CESARO MEANS OF FOURIER–WALSH SERIES. Proceedings of the YSU A: Physical and Mathematical Sciences, 50(1 (239), 64–66. https://doi.org/10.46991/PSYU:A/2016.50.1.064

Issue

Section

Short Communications