Ivashchuk Y. Extreme and approximate properties of unisolvent family functions

The dissertation is devoted to the investigation of two classes of problems concerning the most suitable uniform approximation of ana-logue functions by finite order interpolation classes. The dissertation consists of two parts. The first part investigates the existence and extremal properties of k-snakes - generalization of polynomial notion, having k-linkage with the slightest inflection from zero in the uniform norm.The second part of work deals with the investigation of operator properties of the most suitable approximation by elements of unisolvent family. The dissertation also investigates algorithm development of the most suitable uniform approximation by elements of unisolvent family.