Serdyuk A. Extremal problems of approximation theory on classes of periodic functions.

Dissertation is devoted to the investigation of classical extremal problems of approximation theory on classes of periodic function defined by means of convolutions with fixed generating kernels. Dissertation consists new results on exact values of widths and best approximations by trigonometric polynomials of classes of periodic functions of high smoothness in uniform and integral metrics. Asymptotically unimprovable estimates are obtained for approximations of classes of periodic functions by polynomials generated by some important linear methods of summation of their Fourier series or definite interpolation processes in metrics of spaces C and L_p. Direct and inverse theorems are found of approximation theory of functions in spaces S^p introduced by O.I.Stepanets.