The distribution of extreme points in best complex polynomial approximation (Q917833)

The authors study the problem of uniform approximation by polynomials of a function f continuous on a compact set K with connected complement and analytic in \(\overset \circ K\). They show that Fekete subsets of extremal points \(z\in K:| f(z)-P^*_ n(f;z)| =\| f-P^*_ n\|_ K,\) where \(P^*_ n\) is the best approximant to f of degree n, behave like equilibrium mass distribution on \(\partial K\) for infinitely many n. Also, those results are extended to the weighted approximation.