Geodesic
On absolute and unconditional convergence of series in the general Franklin system
Izvestiya. Mathematics , Tome 73 (2009) no. 2, pp. 279-300

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We prove that, for any admissible sequence, the corresponding general Franklin system $\{f_n(x)\}_{n=0}^{\infty}$ possesses the following property. A series $\sum_{n=0}^{\infty}a_nf_n(x)$ is absolutely convergent almost everywhere on a set $E$ if and only if it is unconditionally convergent almost everywhere on $E$.
Keywords: series, general Franklin system, absolute convergence, unconditional convergence. 
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     author = {G. G. Gevorkyan and K. A. Kerian},
     title = {On absolute and unconditional convergence of series in the general {Franklin} system},
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     number = {2},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2009_73_2_a1/}
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G. G. Gevorkyan; K. A. Kerian. On absolute and unconditional convergence of series in the general Franklin system. Izvestiya. Mathematics , Tome 73 (2009) no. 2, pp. 279-300. http://geodesic.mathdoc.fr/item/IM2_2009_73_2_a1/