On the density of polynomials under perturbations of the measure

Abstract

This paper presents an erroneous proof that if the polynomials are dense in $L_2(\mathbb{R},\rho )$, then they are dense in $L_2(\mathbb{R},\rho +\mu )$ where $\mu$ is a measure supported on a finite set of points.

This paper has been withdrawn by the author. The proof of Lemma 3.2 contains a crucial error and, therefore, the main result of the paper does not hold