Geodesic
Convergence and divergence systems
Matematičeskie zametki, Tome 4 (1968) no. 3, pp. 253-260 
V. F. Gaposhkin. Convergence and divergence systems. Matematičeskie zametki, Tome 4 (1968) no. 3, pp. 253-260. http://geodesic.mathdoc.fr/item/MZM_1968_4_3_a0/
@article{MZM_1968_4_3_a0,
     author = {V. F. Gaposhkin},
     title = {Convergence and divergence systems},
     journal = {Matemati\v{c}eskie zametki},
     pages = {253--260},
     year = {1968},
     volume = {4},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1968_4_3_a0/}
}
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JO  - Matematičeskie zametki
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UR  - http://geodesic.mathdoc.fr/item/MZM_1968_4_3_a0/
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%J Matematičeskie zametki
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Voir la notice de l'article provenant de la source Math-Net.Ru

A generalization of Carleson's theorem concerning series with respect to systems $\{\varphi(nx)\}$ is proved for the case in which $\varphi(x)$ can be expanded in an absolutely convergent Fourier series. Systems corresponding to functions $\varphi(x)$ which have lacunary Fourier series are studied in detail.