The growth of polynomials outside of a compact set-the Bernstein-Walsh inequality revisited (Q2406894)

In this paper, the author presents a new and very simple proof of the classical Bernstein-Walsh inequality. The proof is based on some well-known properties of the Green function and its representation for inverse polynomial images. By modifying this proof, the author obtains a sharper upper bound for \(|Q_n(z)|/\| Q_n\|_K\) in case that \(K\) is real and \(Q_n\) has real coefficients. Moreover the special case of two intervals is discussed.