Sharp estimates for the convergence rate of Fourier series in terms of orthogonal polynomials in L 2((a, b), p(x))

Abstract

Sharp estimates are given for the convergence rate of Fourier series in terms of classical orthogonal polynomials in some classes of functions characterized by a generalized modulus of continuity in the space L 2((a, b), p(x)). Expansions in terms of Laguerre, Hermite, and Jacobi polynomials are considered.