Weighted Approximation with Varying Weight

A new construction is given for approximating a logarithmicpotential by a discrete one. This yields a new approach toapproximation with weighted polynomials of the formw"n"(" "= uppercase)P"n"(" "= uppercase). The new techniquesettles several open problems, and it leads to a simpleproof for the strong asymptotics on some L p(uppercase)extremal problems on the real line with exponential weights,which, for the case p=2, are equivalent to power- typeasymptotics for the leading coefficients of theco