Sharpness-optimal quadrature formulas for the computation of the Fourier transform of finite functions of the class \(C_{L,N}\) (Q1084276)

Sharpness-optimal quadrature formulas are constructed for the computation of integrals of the form \(\int^{b}_{a}f(x)\sin (wx)dx\) and \(\int^{b}_{a}f(x)\cos (wx)dx\) where \(f(x)\in C_{L,N}\), the class of functions that satisfy the Lipschitz condition on [a,b] and take preassigned values \(f_ i=f(x_ i)\), \(i=0,1,...,N-1\), at the points of a given partition. This article is a continuation of two previous articles of the first author and considers the case of strong oscillation of the integrand.