Zherebko T. Uniform approximation of analytic functions

The thesis contains some new results on uniform approximation: polynomial approximation of analytic functions in the domains with piecewise smooth boundary and approximation of conformal mapping of the domain with piecewise smooth boundary onto a disk. Thus, it the uniform weight estimate for analytic functions polynomial approximation was proved and the approximative characteristic for uniform analytic functions approximation in the domains with piecewise smooth boundary was established. Using the methods of V. K. Dziadyk's constructive approximation theory, the uniform approximation estimate of conformal mapping of the domain onto the disk and the pointwise approximation estimate of conformal mapping of the domain onto the disk with the interpolation at the angle's points were obtained .