On the density of polynomials under perturbations of the measure

Rafael del Rio, Luis O. Silva

Published 2015-06-23Version 1

We prove 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. In particular, it will follow that $ \rho+\mu$ is a spectral measure of a Jacobi operator if $\rho$ is. These results are obtained through the analysis of the Green functions of Jacobi operators.