Bernstein's problem on weighted polynomial approximation

2011/10/12 by Alexei Poltoratski, Poltoratski, Alexei
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #math.CV

paper · pdf · doi:10.48550/arxiv.1110.2540

arxiv created 2011/10/28 · arxiv updated 2011/11/01

Abstract

We formulate and discuss 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).

Related

• Smoothing of weights in the Bernstein approximation problem
• De Branges' theorem on approximation problems of Bernstein type
• Polynomial approximation in L_p(R, dμ). I
• On weighted polynomial approximation
• Polynomial approximation on a compact subset of the real line