Geodesic
On a theorem of M. V. Keldysh concerning pointwise convergence of a sequence of polynomials
Sbornik. Mathematics, Tome 52 (1985) no. 2, pp. 553-555 Cet article a éte moissonné depuis la source Math-Net.Ru

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This article contains a proof of the following fact: for any bounded function $f(z)$, $|z|=1$, of the first Baire class such that $\int_{|z|=1}f(z)z^n\,dz=0$ for $n=0,1,\dots$, there exists a uniformly bounded sequence of polynomials on $|z|=1$ converging pointwise to $f(z)$. Bibliography: 2 titles. 
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     author = {S. V. Kolesnikov},
     title = {On a~theorem of {M.} {V.~Keldysh} concerning pointwise convergence of a~sequence of polynomials},
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     year = {1985},
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     url = {http://geodesic.mathdoc.fr/item/SM_1985_52_2_a14/}
}
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S. V. Kolesnikov. On a theorem of M. V. Keldysh concerning pointwise convergence of a sequence of polynomials. Sbornik. Mathematics, Tome 52 (1985) no. 2, pp. 553-555. http://geodesic.mathdoc.fr/item/SM_1985_52_2_a14/

[1] Keldysh M. V., “Stir les suites de polynômes bornes dans leur ensemble”, Matem. sb., 42(84) (1935), 719–724 | Zbl

[2] Iosida K., Funktsionalnyi analiz, Mir, M., 1963 | MR