Geodesic
On unconditional and absolute convergence of wavelet type series
Fundamentalʹnaâ i prikladnaâ matematika, Tome 6 (2000) no. 1, pp. 81-92 
S. V. Golovan'. On unconditional and absolute convergence of wavelet type series. Fundamentalʹnaâ i prikladnaâ matematika, Tome 6 (2000) no. 1, pp. 81-92. http://geodesic.mathdoc.fr/item/FPM_2000_6_1_a7/
@article{FPM_2000_6_1_a7,
     author = {S. V. Golovan'},
     title = {On unconditional and absolute convergence of wavelet type series},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {81--92},
     year = {2000},
     volume = {6},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2000_6_1_a7/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we consider wavelet type systems, i. e. systems of type $$ \{\psi_{mn}(x)=2^{m/2}\psi(2^mx-n)\}, $$ where $\psi\in L^2(\mathbb R)$ such that $\operatorname{supp}\psi\Subset\mathbb R$. Let $E$ be a set of real numbers. We prove the equivalence of absolute and unconditional convergence almost everywhere on $E$ of the series $$ \sum_{\substack{m\geq 0\\ n\in\mathbb Z}}a_{mn}\psi_{mn}(x) . $$