Bernstein's problem on weighted polynomial approximation
  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 $\mu$ on the real line we give a criterion for density of polynomials in $L^p(\mu)$. 
Alexei Poltoratski
math.CV