Geodesic
On the selection of a convergence subsystem with logarithmic density
Sbornik. Mathematics, Tome 64 (1989) no. 1, pp. 41-56 
G. A. Karagulian. On the selection of a convergence subsystem with logarithmic density. Sbornik. Mathematics, Tome 64 (1989) no. 1, pp. 41-56. http://geodesic.mathdoc.fr/item/SM_1989_64_1_a2/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Theorems are proved on the selection of convergence subsystems and $S_p$-subsystems with lacunary index density. Bibliography: 10 titles.

[1] Menchoff D., “Sur la convergence et la sommation des séries de fonctions orthogonales”, Bull. Soc. Math. France, 64 (1936), 147–170 | MR | Zbl

[2] Marcinkiewicz J., “Sur la convergence des séries orthogonales”, Studia Math., 6 (1936), 39–45 | Zbl

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

[4] Kachmazh S., Shteingauz G., Teoriya ortogonalnykh ryadov, Fizmatgiz, M., 1958 | MR

[5] Bennett G., “Lecture on matrix transformation of $l^p$-spaces”, Notes in Banach spaces, ed. H. E. Lacey, University of Texas Press, Austin, 1980 | MR

[6] Kashin B. S., “O vybore podsistemy skhodimosti iz dannoi ortonormirovannoi sistemy”, UMN, 40:2 (1985), 181–182 | Zbl

[7] Agaev I., “Lacunary subsets of orthonormal sets”, Analysis Math., 11 (1985), 283–301 | DOI | MR | Zbl

[8] Nevë Zh., Matematicheskie osnovy teorii veroyatnostei, Mir, M., 1969 | MR

[9] Yaglom A. M., Yaglom I. M., Neelementarnye zadachi v elementarnom izlozhenii, Gostekhizdat, M., 1954 | MR

[10] Agaev I., “O vybore podsistem skhodimosti iz dannoi ortonormirovannoi sistemy”, Soobsch. AN GSSR, 121:1 (1986), 45–48 | MR | Zbl