On the Approximative Properties of Fourier Series in Laguerre–Sobolev Polynomials

Abstract

Considering the approximation of a function \( f \) from a Sobolev space by the partial sums of Fourier series in a system of Sobolev orthogonal polynomials generated by classical Laguerre polynomials, we obtain an estimate for the convergence rate of the partial sums to \( f \).