Applications (e.g. in signal processing) motivate the following problem:
Given sufficiently many evaluations of a linear combination of exponential functions, determine its support, i.e., the set of exponentials occurring with non-zero coefficient.
A classic tool to attack this problem is Prony's method to compute polynomials defining (the base points of elements of) the support. This applies to exponentials over arbitrary fields and can thus be seen as a purely algebraic method.
In this talk we propose a framework encompassing recently studied variants and extensions of Prony's method and clarifying relations between them. This includes multivariate Hankel as well as Toeplitz variants for several classes of functions. We also discuss the relative case taking given polynomial equations for the support into account.
The talk is based on a recent joint work with Stefan Kunis and Tim Römer.