Bernstein’s Problem on Weighted Polynomial Approximation

Abstract

AbstractWe formulate a necessary and sufficient condition for polynomials to be dense in a space of continuous functions on the real line, with respect to Bernstein’s weighted uniform norm. Equivalently, for a positive finite measure μ on the real line we give a criterion for density of polynomials in L p(μ).KeywordsWeighted Polynomial ApproximationClark MeasureBorichevKoosisPointmassThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.