Finite-infinite-range inequalities in the complex plane (Q1187059)

In this paper, the author derives analogues in the plane of the infinite- finite range inequalities that have had so many applications for weighted approximation on the real line. He considers a set \(E\subseteq\mathbb{C}\) and a weight \(w:E\to[0,\infty)\) and investigates the subset \(K\) of \(E\) on which weighted polynomials of the form \(w^ nP_ n\) (degree of \(P_ n\leq n)\) ``live''. This will be of interest to those working in weighted approximation in the plane.