Universality of multivariate interpolation

摘要

The aim of this article is to generalize the theory of functions "universal" with respect to interpolation operators from the univariate case introduced by Vogt [6, 7] to the multivariate situation. Therefore, new arguments and different function spaces beyond mere polynomials are investigated to obtain functions / which have the following property: If one interpolates them in a certain sequence of nodal sets under certain conditions, the sequence of interpolating functions or some multiples of them allows uniform (or even stricter) approximation of any continuous function, or from a certain substantial subset of those, by a suitable subsequence.