Approximation of Function and Its Derivative from the Hölder–Lipschitz Class by Their Fourier Coefficients for the Harmonically Modulated Argument

A proof is given of theorems according to which any function and its derivative belonging to the Hölder–Lipschitz class Сα (G) can be approximated with any predetermined accuracy by a finite sum of dependences of the Fourier coefficients for a harmonically modulated argument of the fu-nction.