Functional differentiation of integral operators of special form and some questions of the inverse interpolation

This article is devoted to the problem of operator interpolation and functional differentiation. Some information about variational derivatives explicit formulas for exact solutions simplest equations containing first required are given. For functionals defined on sets functions square matrices, various interpolating polynomials Hermitе type with nodes second multiplicity, which contain interpolated operator, constructed. The presented problems based algebraic Chebyshev system functions. analytic an argument from a set antiderivatives obtained. solution some differential integral operators special form found. inverse considered. Explicit schemes constructing functionals, including case matrix variable, obtained using certain well-known results theory, demonstrated. Data representation illustrated by number examples.