On the Regularity of Multivariate Hermite Interpolation Original Research Article

In this paper a result due to Gevorgian, Sahakian, and the author concerning the regularity of bivariate Hermite interpolation is generalized in two directions: in the bivariate case and for arbitrary dimensions. Also a notion of independence (preregularity) of interpolation conditions is discussed and a relation on the independence on different dimensions is indicated. As corollaries combinatorial inequalities are obtained. At the end a pair of related number inequalities is presented.