On a theorem of M. V. Keldysh concerning pointwise convergence of a sequence of polynomials

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.