The aim of this paper is to study many interpolation problems in the space of polynomials of w-degree n. In order to do this, some new results concerning the polynomial spaces of w-degree n are given. We consider only the case of functions in two variables, but all the results obtained can be easily extended to many variables. We found a set of conditions for which, Πn,w, the space of polynomia...

In this contribution, we study multivariate polynomial interpolation and quadrature rules on non-tensor product node sets linked to Lissajous curves and Chebyshev varieties. After classifying multivariate Lissajous curves and the interpolation nodes related to these curves, we derive a discrete orthogonality structure on these node sets. Using this discrete orthogonality structure, we can deriv...