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Let K be a compact set in the complex plane having connected and regular complement, and let f be any function continuous on K and analytic in the interior of K. For the polynomials p* (f) of respective degrees at most n of best uniform approximation to f on K, we investigate the density of the sets of extreme points An(f):= {z E K: If (z))-Pn(f)(Z)I = Ilf -Pn*(f)IIK } in the boundary of K.

The density of extreme points in complex polynomial approximation