On the regularity of multivariate Hermite interpolation (Q1577533)

In this paper, former joint studies of Gevorgian, Sahakian and the author concerning multivariate Hermite interpolation are continued. Consider \(n_1,\dots,n_s\) to be a set of multiplicities, and let \(n\) denote the maximal total degree of the interpolating polynomials. Then the scheme \({\mathcal N}=\{n_1, \dots, n_s;n\}\) is said to be independent, if for some set of nodes the corresponding Hermite interpolation problem is solvable for any given set of data. In the main Theorem, a sufficient condition for independence of a scheme \({\mathcal N}\) (together with appropriate sets of nodes) is given. The theorem turns out to be a generalization of a former result of the authors mentioned above concerning bivariate Hermite interpolation [\textit{H. V. Gevorgian}, \textit{H. A. Hakopian} and \textit{A. A. Sahakian}, Constructive Approximation 11, No. 1, 23-36 (1995; Zbl 0823.41004)]. As corollaries, combinatorial inequalities are obtained.