To the interpolation theory of differential operators of arbitrary order in partial derivatives

This article is devoted to the problem of construction and research of the Lagrange interpolation formulas and formulas of the Hermite type with nodes of the second multiplicity for differential operators of arbitrary order in partial derivatives given in the space of continuously differentiable functions of many variables. The construction of operator interpolation formulas is based on interpolation polynomials for scalar functions with respect to the arbitrary Chebyshev system of functions. An explicit representation of the interpolation error has been obtained.