International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Issue 12, Article ID 53474, 20 pages
doi:10.1155/IJMMS/2006/53474

Least squares approximations of power series

Abstract

The classical least squares solutions in C[−1,1] in terms of linear combinations of ultraspherical polynomials are extended in order to estimate power series on (−1,1). Approximate rates of uniform and pointwise convergence are obtained, which correspond to recent results of U. Luther and G. Mastroianni on Fourier projections with respect to Jacobi polynomials.