Approximation of the function and its derivative relating to the Hölder–Lipschitz class with their Fourier coefficients for a harmonically modulated argument

The paper considers the proved theorems according to which any function and its derivative relating to the Hölder–Lipschitz class $C^\alpha(G)$ can be approximated with any pre-set accuracy by a finite sum of the dependences of the Fourier coefficients for a harmonically modulated function argument.