Least squares approximations of power series (Q2468996)

Summary: 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 \textit{U. Luther} and \textit{G. Mastroianni} on Fourier projections with respect to Jacobi polynomials [in: Problems and methods in mathematical physics. The Siegfried Prössdorf memorial volume. Proceedings of the 11th TMP conference, Chemnitz, Germany, March 25-28, 1999. Oper. Theory, Adv. Appl. 121, 327--351 (2001; Zbl 1001.42014)].