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Autumn 2018 On behavior of Fourier coefficients and uniform convergence of Fourier series in the Haar system
M. G. ‎Grigoryan‎, A. Kh. ‎Kobelyan
Adv. Oper. Theory 3(4): 781-793 (Autumn 2018). DOI: 10.15352/aot.1801-1300

Abstract

‎Suppose that $\hat{b}_m\downarrow 0,\ \{\hat{b}_m\}_{m=1}^\infty\notin l^2,$‎ ‎and $b_n=2^{-\frac{m}{2}}\hat{b}_m$ for all $ n\in(2^m,2^{m+1}].$‎ ‎In this paper‎, ‎it is proved that any measurable and almost everywhere finite‎ ‎function $f(x)$ on $[0,1]$ can be corrected on a set of arbitrarily small measure‎ ‎to a bounded measurable function $\widetilde{f}(x)$; so that the nonzero Fourier-Haar‎ ‎coefficients of the corrected function present some subsequence of $\{b_n\}$‎, ‎and its‎ ‎Fourier-Haar series converges uniformly on $[0,1]$‎.

Citation

Download Citation

M. G. ‎Grigoryan‎. A. Kh. ‎Kobelyan. "On behavior of Fourier coefficients and uniform convergence of Fourier series in the Haar system." Adv. Oper. Theory 3 (4) 781 - 793, Autumn 2018. https://doi.org/10.15352/aot.1801-1300

Information

Received: 21 January 2018; Accepted: 12 May 2018; Published: Autumn 2018
First available in Project Euclid: 8 June 2018

MathSciNet: MR3856172
Digital Object Identifier: 10.15352/aot.1801-1300

Subjects:
Primary: 42A65
Secondary: 42A20, 43A50

Rights: Copyright © 2018 Tusi Mathematical Research Group

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Vol.3 • No. 4 • Autumn 2018
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