Polynomial approximation in L_p(R, dμ). I

1998/10/16 by Andrew G. Bakan, Bakan, Andrew G.
Mathematics · #30D10 #30D45 #41A10 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:30D10 #msc:30D45 #msc:41A10

paper · pdf · doi:10.48550/arxiv.math/9810104

LaTeX, amsfonts, 45 p

arxiv created 1998/10/16 · arxiv updated 2009/11/30

Abstract

Final representation of all those measures μ for which algebraic polynomials are dense in L_p(R, dμ) is found. The weighted analogue of the Weierstrass polynomial approximation theorem and a new version of the M. Krein's theorem about partial fraction decomposition of reciprocal of an entire function are established.

Related

• Bernstein's problem on weighted polynomial approximation
• On weighted polynomial approximation
• On the density of polynomials under perturbations of the measure
• Low rank approximation of polynomials
• On weighted approximation with Jacobi weights