Demkiv I. Interpolation of nonlinear operators on the continual set of knots

The thesis is devoted to the construction and investigation of interpolation formulas of both polynomial type and chain fractions for nonlinear functionals and operators with partially known and completely unknown structure on the set of continual knots. A simple operator polynomial approximation for the Urison operator with unknown kernel was constructed and investigated. Necessary and sufficient conditions for the existence of a single functional interpolation Newton type polynomial on the continual set of knots are found. The following problems: interpolation of functionals with many variables in linear topological spaces and in the space with continual knots, a polynomial interpolation in Banach space with a basis in the space and Hilbert space are solved. Interpolation integral chain fractions for nonlinear functionals are constructed and investigated. These fractions are natural generalization of interpolation chain fractions for functions of one and two variables. On the basis of constructed Newton type interpolation formulas interpolation formulas of Hermite type are constructed and investigated.