Remarks on interpolation in certain linear spaces (IV) - Adrian Diaconu (Journal of numerical analysis and approximation theory, 2007)
In the papers [5], [6], [7] we shall study a way of extending the model of interpolating the real functions, with simple nodes, to the case of the functions defined between linear spaces, especially between linear normed spaces. In order to keep as many characteristics as possible from the case of the interpolation of real functions, in this paper we present a model of construction of the abstract interpolation polynomials and the divided differences based on the properties of multilinear mappings. The aim of the present paper is the study of the conduct of the abstract interpolation polynomial, in the case when the function for interpolation is a abstract polynomial. In the last part we will construct the abstract interpolation polynomial and the divided differences, in the case in which the spaces \(X\) and \(Y\) have finite dimensions.