Title:
Sparse decomposition from moments.

Abstract:
In 1795, G. de Prony proposed a method to decompose a function as a sum of exponentials from values at regularly spaced points. We show how this problem is naturaly connected to polynomials and Hankel matrices.
We describe a multivariate extension of the method based of a generalization of Kronecker theorem for Hankels operators of finite rank, its relation with sparse decomposition and give some applications to tensor decomposition.