Geodesic
On~polynomial approximation of functions on Hilbert space
Sbornik. Mathematics, Tome 21 (1973) no. 2, pp. 255-277

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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. 
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     author = {A. S. Nemirovskii and S. M. Semenov},
     title = {On~polynomial approximation of functions on {Hilbert} space},
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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/