Multivariate Polynomial Interpolation to Traces on Manifolds Original Research Article

A necessary and sufficient condition for polynomials defined on some (proper or improper) linear manifolds on Rk is given in order that they agree there with the traces of a polynomial on Rk (see H. A. Hakopian and A. A. Sahakian, in "Abstracts, International Workshop on Multivariate Interpolation and Approximation, Duisburg, 1989"). An inductive construction of this interpolating polynomial is obtained. The analogous interpolation on the sphere and with homogeneous polynomials is also presented, and some connections with other multivariate and finite element interpolations are explored.