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
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
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