APPROXIMATIVE PROPERTIES OF FOURIER-MEIXNER SUMS

Abstract

We consider the problem of approximation of discrete functions f = f(x) defined on the set Ω_δ = {0, δ, 2δ, . . .}, where δ =1/N, N > 0, using the Fourier sums in the modified Meixner polynomials M_(α;n,N)(x) = M(α;n)(Nx) (n = 0, 1, . . .), which for α > -1 constitute an orthogonal system on the grid Ωδ with the weight function w(x) = e^-(x)*Γ(Nx + α + 1)/Γ(Nx + 1). We study the approximative properties of partial sums of Fourier series in polynomials M(α_n,N)(x), with particular attention paid to estimating their Lebesgue function.

Keywords

• Ixner polynomials ◆ Fourier series ◆ Lebesgue function