S. V. Kolesnikov, “On a theorem of M. V. Keldysh concerning pointwise convergence of a sequence of polynomials”, Mat. Sb. (N.S.), 1984, Volume 124(166), Number 4(8),Pages <nobr>568

This article is cited in 6 papers

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

S. V. Kolesnikov

Abstract: 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.

UDC: 517.5+517.98

MSC: 41A10, 30B60, 30C10

Received: 15.02.1984