Geodesic
Existence of a basis in the space of functions analytic in the disk, and some properties of Franklin's system
Sbornik. Mathematics, Tome 24 (1974) no. 1, pp. 1-16 
S. V. Bochkarev. Existence of a basis in the space of functions analytic in the disk, and some properties of Franklin's system. Sbornik. Mathematics, Tome 24 (1974) no. 1, pp. 1-16. http://geodesic.mathdoc.fr/item/SM_1974_24_1_a0/
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is shown that there is a basis in the space of functions analytic in the unit disk and continuous in the closed unit disk. This answers a question posed by Banach. It is further shown that the Franklin system is an unconditional basis in the spaces $L_p(0,1)$ for $1. Bibliography: 8 titles.

[1] S. Banach, Théorie des opérations linéaires, Warszawa, 1932

[2] Ph. Franklin, “A set of continuous orthogonal functions”, Math. Ann., 100 (1928), 522–529 | DOI | MR | Zbl

[3] Z. Ciesielski, “Properties of the orthonormal Franklin system”, Studia Math., 23:2 (1963), 141–157 | MR | Zbl

[4] Z. Ciesielski, “Properties of the orthonormal Franklin system, II”, Studia Math., 27:3 (1966), 289–323 | MR | Zbl

[5] A. Zigmund, Trigonometricheskie ryady, t. 1, izd-vo «Mir», Moskva, 1965 | MR

[6] Dzh. Alberg, E. Nilson, Dzh. Uolsh, Teoriya splainov i ee prilozheniya, izd-vo «Mir», Moskva, 1972 | MR

[7] A. Zygmund, “On a theorem of Marcinkiewicz concerning interpolation of operators”, J. Math. Pure et Appl., 35 (1956), 223–248 | MR | Zbl

[8] S. V. Bochkarev, “O bezuslovnykh bazisakh”, Matem. zametki, 1:4 (1967), 391–398 | Zbl