Asymptotic estimates for the generalized Fourier coefficients

摘要

Explicit forms for the orthonormal polynomials with respect to a given weight function on the interval [−1, 1] usually are difficult to construct. In this paper we give asymptotic estimates for the generalized Fourier coefficients of functions expanded in series of certain nonclassical orthonormal polynomials without requiring explicit forms of these orthonormal polynomials. Estimates for the generalized Fourier coefficients can be applied to the weighted least squares approximation.