On the density of polynomials under perturbations of the measure

Rafael del Rio; Luis O. Silva

On the density of polynomials under perturbations of the measure

Mathematical Physics 2015-06-30 v2 math.MP

Authors: Rafael del Rio , Luis O. Silva

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.

Keywords

polynomial density L2 space measure perturbation finite support measure approximation theory functional analysis

Cite

@article{arxiv.1506.07162,
  title  = {On the density of polynomials under perturbations of the measure},
  author = {Rafael del Rio and Luis O. Silva},
  journal= {arXiv preprint arXiv:1506.07162},
  year   = {2015}
}

Comments

This paper has been withdrawn by the author.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

On the density of polynomials under perturbations of the measure

Abstract

Keywords

Cite

Comments

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