A characterization of smoothness for Freud weights (Q1298587)

In this paper, the author studies the rate (or degree) of approximation by weighted polynomials \(P_nW\), where \(P_n\) is a polynomial of degree \(\leq n\), and \(W\) is a Freud weight, such as \(\exp(-| x |^\alpha)\), \(\alpha>1\). Building on earlier work on Jackson and Bernstein theorems for weighted moduli of continuity, the author provides a more precise characterization of some specific rates of approximation. The description of the results involves moduli of continuity and also derivatives of polynomials of best approximation.