Haievskii M. Problems of approximation of analytic bar{psi}-differentiable functions.

Investigated in the thesis are the following classes of continuous periodic functions C^{bar{psi}}C, analytic in a circle H^psi_infty and analytical functions in areas A(overline{Omega}). Obtained here are estimates deviations of Fourier sums on the spaces C^{bar{psi}} and the estimates deviations Taylor's sums on classes of analytic functions H^psi_infty. In this work estimates group of deviations of Fourier sums on the spaces C^{bar{psi}} expressed in terms of the best approximation of bar{psi}-derivatives of functions and estimates convergence groups varphi-deviations and lambda-method summation Taylor series of analytic and bounded functions in the unit circle are found. The work specifies the necessary and sufficient conditions for the regularity of summation method for the class of functions that are analytic on a unit disk and continuous on a closed circle. The exact order estimates of the deviations of analytic functions, which are defined in a bounded domain and which are continuous on its closure, of their sums Zigmund are obtained.