Abstract
We show that ifw(x)=exp(−|x|λ), then in the case λ=1 for every continuousf that vanishes outside the support of the corresponding extremal measure there are polynomialsPn of degree at mostn such thatwnPn uniformly tends tof, and this is not true when λ<1. These are the missing cases concerning approximation by weighted polynomials of the formwnPn wherew is a Freud weight. Our second theorem shows that even if we are only interested in approximation off on the extremal support, the functionf must still vanish at the endpoints, and we actually determine the (sequence of) largest possible intervals where approximation is possible. We also briefly discuss approximation by weighted polynomials of the formW(anx)Pn(x).
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