Short proofs of some theorems in approximation theory (Q1433344)

The author of the paper under review proposes new proofs of three well known results in polynomial approximation. In particular, a new proof of the following result is given: Let \(f\) be a function holomorphic in the disk \(\rho\mathbb{D}\) of radius \(\rho>1\) such that \(|f(z)|\leq\mu\), \(|z|< \rho\). If \(E_N\) is the definition from \(f\) to the set of polynomials of degree \(N\) in the uniform norm on \(\mathbb{D}\), then \(E_n(f)\leq\frac {M} {\rho^{N+1}}\).