Geodesic
On the extraction, from general systems, of lacunary subsystems with the absolute convergence property
Sbornik. Mathematics, Tome 39 (1981) no. 4, pp. 469-477 
R. I. Ovsepian. On the extraction, from general systems, of lacunary subsystems with the absolute convergence property. Sbornik. Mathematics, Tome 39 (1981) no. 4, pp. 469-477. http://geodesic.mathdoc.fr/item/SM_1981_39_4_a2/
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     title = {On the extraction, from general systems, of lacunary subsystems with the absolute convergence property},
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This paper considers the problem of extracting lacunary subsystems from general sequences of functions. In particular, it is shown that every orthonormal system contains a Sidon subsystem. Bibliography: 7 titles.

[1] V. F. Gaposhkin, “Lakunarnye ryady i nezavisimye funktsii”, Uspekhi matem. nauk, XXI:6(132) (1966), 3–82

[2] S.Szidon, “Über Orthogonalsysteme”, Comp. Math., 7 (1940), 372–375 | MR

[3] S. Szidon, “Über Orthogonalen Entwicklungen”, Acta Math. Szeged, 10 (1943), 206–253 | MR

[4] J. Marcinkiewicz, “Sur les series orthogonales”, Studia Math., 8 (1939), 1–27 | MR | Zbl

[5] V. Ya. Kozlov, “O raspredelenii polozhitelnykh i otritsatelnykh znachenii ortogonalnykh i normirovannykh funktsii, obrazuyuschikh polnuyu sistemu”, Matem. sb., 23(65) (1948), 475–480 | MR | Zbl

[6] F. G. Arutyunyan, “O raspredelenii polozhitelnykh i otritsatelnykh znachenii funktsii, obrazuyuschikh bezuslovnyi bazis v prostranstve $L^p(0,1)$”, Izv. AN Arm. SSR, Matematika, 1:1 (1966), 79–87 | MR | Zbl

[7] O. A. Ziza, “O podsistemakh sistemy mnozhestv”, Matem. zametki, 17:3 (1975), 485–495 | MR | Zbl