It is proven that if xQ′(x) is increasing on (0,+∞) and w(x) = exp(−Q) is the corresponding weight on [0,+∞), then every continuous function that vanishes outside the support of the extremal measure associated with w can be uniformly approximated by weighted polynomials of the form wPn. This problem was raised by V. Totik, who proved a similar result (the Borwein-Saff conjecture) for convex Q. A general criterion is introduced, too, which guarantees that the support of the extremal measure is… CONTINUE READING