Geodesic
On polynomial approximation of functions on Hilbert space
Sbornik. Mathematics, Tome 21 (1973) no. 2, pp. 255-277 
A. S. Nemirovskii; S. M. Semenov. On polynomial approximation of functions on Hilbert space. Sbornik. Mathematics, Tome 21 (1973) no. 2, pp. 255-277. http://geodesic.mathdoc.fr/item/SM_1973_21_2_a5/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper the question is considered of uniform approximation by polynomials and smooth functions of uniformly continuous functions given on the unit ball of countable-dimensional Hilbert space. Bibliography: 8 titles.

[1] V. I. Averbukh, O. G. Smolyanov, “Teoriya differentsirovaniya v lineinykh topologicheskikh prostranstvakh”, Uspekhi matem. nauk, XXII:6 (138) (1967), 201–260

[2] Dzh. Ills, “Osnovaniya globalnogo analiza”, Uspekhi matem. nauk, XXIV:3 (147) (1969), 157–210 | MR

[3] P. Levi, Konkretnye problemy funktsionalnogo analiza, izd-vo «Nauka», Moskva, 1967 | MR

[4] A. S. Nemirovskii, “Ob odnoi tsepochke algebr na gilbertovom share”, Funkts. analiz, 5:1 (1971), 85–86 | MR | Zbl

[5] A. S. Nemirovskii, Gladkaya i polinomialnaya approksimatsiya nepreryvnykh funktsii na gilbertovom prostranstve, Dissertatsiya, MGU, Moskva, 1973

[6] S. M. Semenov, “O polinomakh na lineinykh topologicheskikh prostranstvakh”, Vestnik MGU, matem. mekhan., 1970, no. 3, 45–49 | MR | Zbl

[7] S. M. Semenov, “Ob algebrakh na gilbertovom prostranstve, porozhdennykh kvadratichnymi formami”, Funkts. analiz, 5:2 (1971), 89–90 | MR | Zbl

[8] S. M. Semenov, Simmetricheskie funktsii na prostranstvakh $L_p$, Dissertatsiya, MGU, Moskva, 1973