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

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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},
     journal = {Sbornik. Mathematics},
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     volume = {52},
     number = {2},
     year = {1985},
     language = {en},
     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/