Geodesic
On asymptotically best lacunary systems
Izvestiya. Mathematics , Tome 1 (1967) no. 5, pp. 967-982.

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Asymptotically best lacunary systems are introduced and investigated. Best lacunary subsystems (in the sense of $({}^1)$) for the trigonometric system and the Walsh system are also investigated. 
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V. F. Gaposhkin. On asymptotically best lacunary systems. Izvestiya. Mathematics , Tome 1 (1967) no. 5, pp. 967-982. http://geodesic.mathdoc.fr/item/IM2_1967_1_5_a3/

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[3] Banach S., “Sur les séries lacunaires”, Bull. Acad. polon. Sci., 1933, 149–154 | Zbl

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

[6] Zigmund A., Trigonometricheskie ryady, GONTI, M., L., 1939