OPTIMAL QUADRATURE EVALUATION OF INTEGRALS OF RAPIDLY OSCILLATING FUNCTIONS IN LIPSCHITZ INTERPOLATION CLASS IN CASE OF STRONG OSCILLATION

摘要

An accuracy-optimal quadrature formula is derived to evaluate the Fourier transform of compact functions from an interpolation Lipschitz class. The case of strong oscillation of the integrand is considered. The optimality is substantiated based on the boundary function method, namely, constructing the Chebyshev center and Chebyshev radius in the uncertainty domain of the problem solution.