On the completeness of algebraic polynomials in the spaces $L_p (ℝ, dμ)$

Abstract

We prove that the theorem on the incompleteness of polynomials in the space $C^0_w$ established by de Branges in 1959 is not true for the space $L_p (ℝ, dμ)$) if the support of the measure μ is sufficiently dense