The general approach to solving extremal problems in various classis of analytic functions, based on duality relations between extremums, was developed. This method was developed also to the investigation extremal problems with supplementary conditions. The general theory such processes of the approximation, when the magnitude of the approximating aggregates take into account, was developed in Banach spaces. Faktorization theory for analytic functions on compact Riemann surfaces with boundary was constructed. The extremal problem analytic capacity in arbitrary domains was investigated and a theory of the extremal problems like the analytic capacity for Golubev sums was constructed. The Chebyshev theorem for the best approximation of a function of two variables by means of sum functions of one variable was proved.
Main publications:
Khavinson S. Ya. Extremal problems in complex analysis // AMS Translations. Series 2, v. 129, 1986, 1–114.
Khavinson S. Ya. Best Approximation by Linear Superpositions (Approximate Nomography) // AMS Translations of Mathem. Monographs. V. 159, 1997, 1–175.
