Geodesic
Bases of the space of continuous functions
Sbornik. Mathematics, Tome 17 (1972) no. 4, pp. 583-602 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper, new bases for the space of continuous functions are constructed, similar to the Schauder basis but having better differentiability properties. The bases constructed are applied to the problem of the order of growth of the degrees of a polynomial basis of the space $C(0,1)$. It is proved that for any nondecreasing sequence of natural numbers $\{\omega(n)\}_{n=0}^\infty$ satisfying the condition $\sum_{n=2}^{\infty}\frac1{n\ln n\omega(n)}<\infty$ it is possible to construct a polynomial basis with order of growth $\nu_n\leqslant n\omega(n)$, $n=0,1,2,\dots$ . Bibliography: 16 titles. 
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Z. A. Chanturiya. Bases of the space of continuous functions. Sbornik. Mathematics, Tome 17 (1972) no. 4, pp. 583-602. http://geodesic.mathdoc.fr/item/SM_1972_17_4_a8/

[1] C. Foias, I. Singer, “Some remarks on strongly lineary independent sequenses and bases in Banach spaces”, Rev. Math. Pures et Appl., VI:3 (1961), 589–594 | MR

[2] P. L. Ulyanov, “O nekotorykh reshennykh i nereshennykh problemakh teorii ortogonalnykh ryadov”, Trudy IV Vsesoyuznogo matem. s'ezda, t. II, Leningrad, 1964, 694–704

[3] P. L. Ulyanov, “Reshennye i nereshennye problemy teorii trigonometricheskikh i ortogonalnykh ryadov”, Uspekhi matem. nauk, XIX:1(115) (1964), 3–69 | MR

[4] K. M. Shaidukov, “O poryadke rosta stepenei polinomialnogo bazisa”, Funkts. analiz i teoriya funktsii, no. 1, Kazan, 1963, 134–138

[5] 3. A. Chanturiya, “Ob odnoi zadache P. L. Ulyanova”, Soobsch. AN Gruz. SSR, 38:3 (1965), 527–528 | Zbl

[6] 3. A. Chanturiya, “K zadache P. L. Ulyanova o poryadke rosta stepenei polinomialnogo bazisa”, Matem. zametki, 1:4 (1967), 415–424 | Zbl

[7] G. Faber, “Uber die interpolatorische Darstellung stetiger Functionen”, Jahresber. Deutshen. Math. Ver., 23 (1914), 192–210 | Zbl

[8] 3. A. Chanturiya, “Ob odnom obobschenii teoremy G. Fabera o polinomialnykh bazisakh”, Matem. zametki, 2:2 (1967), 187–190

[9] Yu. Shauder, “Zur theorie stetiger Abbildungen in funktional Raumen”, Math. Z., 26 (1927), 47–65 | DOI | MR

[10] S. Kachmazh, G. Shteingauz, Teoriya ortogonalnykh ryadov, Fizmatgiz, Moskva, 1958

[11] K. M. Shaidukov, “O bazisakh v prostranstve nepreryvnykh funktsii, postroennykh iz dug parabol”, Funkts. analiz i teoriya funktsii, no. 3, Kazan, 1966, 133–142

[12] R. Kuk, Beskonechnye matritsy i prostranstva posledovatelnostei, Fizmatgiz, Moskva, 1960

[13] A. F. Timan, Teoriya priblizheniya funktsii deistvitelnogo peremennogo, Fizmatgiz, Moskva, 1960

[14] S. Mandelbroit, Primykayuschie ryady. Regulyarizatsiya posledovatelnostei. Primeneniya, IL, Moskva, 1955

[15] I. Singer, Bases in Banach spaces, Springer-Verlag, 1970 | MR

[16] 3. A. Chanturiya, “O bazisakh prostranstva nepreryvnykh funktsii”, DAN SSSR, 187:2 (1969), 284–286 | Zbl