Unconditional convergence almost everywhere of Fourier series of continuous functions in the Haar system
Matematičeskie zametki, Tome 4 (1968) no. 2, pp. 211-220
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A continuous function is constructed whose Haar-Fourier series, after a definite rearrangement of its terms, diverges almost everywhere. A function is also constructed which has the maximum degree of smoothness in the sense that if its smoothness is increased its Haar-Fourier series becomes unconditionally convergent almost everywhere.
@article{MZM_1968_4_2_a12,
author = {S. V. Bochkarev},
title = {Unconditional convergence almost everywhere of {Fourier} series of continuous functions in the {Haar} system},
journal = {Matemati\v{c}eskie zametki},
pages = {211--220},
publisher = {mathdoc},
volume = {4},
number = {2},
year = {1968},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1968_4_2_a12/}
}
TY - JOUR AU - S. V. Bochkarev TI - Unconditional convergence almost everywhere of Fourier series of continuous functions in the Haar system JO - Matematičeskie zametki PY - 1968 SP - 211 EP - 220 VL - 4 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/MZM_1968_4_2_a12/ LA - ru ID - MZM_1968_4_2_a12 ER -
S. V. Bochkarev. Unconditional convergence almost everywhere of Fourier series of continuous functions in the Haar system. Matematičeskie zametki, Tome 4 (1968) no. 2, pp. 211-220. http://geodesic.mathdoc.fr/item/MZM_1968_4_2_a12/