Mykhalchuk B. Interpolation nonlinear functionals by the functional polynomials and integral chain fractions

This dissertation is dedicated to construction and researches the characteristics of the interpolation polynomials and integral chain fractions (ICF) for the functional (from piecewise continuous functions space in real number space) on the continual set of knots. The researching characteristics are: the conditions of existence and unique; retaining of corresponding degree polynomial and integral chain fraction; the continual set of knots and it's role; remainder of series and it's estimate. In this dissertation it was found necessary and sufficient conditions of the functional polynomial existence, which depend with the rule of substitution. For the first time interpolation ICF has been constructed for the functional. Necessary and sufficient conditions were found for interpolation ICF. It was explored the role of interpolation knots continuous in the uniqueness of interpolation ICF. The formula for remainder was found.