Hermite interpolation of type total degree associated with certain spaces of polynomials (Q6550092)

Both Lagrange and Hermite interpolation with polynomials in any dimension with a fixed maximal degree are important tools for the approximation of multivariable functions. An alternative formulation is to carry out these types of interpolation for approximation by homogeneous polynomials, not by polynomial of a given degree. In this paper both approaches are analysed and their properties (e.g., regularity of the problems and their limits) compared.