Hankel and Toeplitz operators of finite rank and Prony's problem in several variables
For researchers in multidimensional signal processing and algebraic computation, this work unifies several previously separate approaches.
The paper establishes the equivalence between Prony's problem in several variables and finite-rank Hankel operators, linking polynomial ideal theory, moment problems, and signal processing.
Prony's problem in several variables has attracted some attention recently and provides an interesting combination of polynomial ideal theory with analytic and numeric computations. This note points out further connections to Hankel operators of finite rank as they appear in multidimensional moment problems, shift invariance signal spaces, annihilating ideals of filters and factorization of the Hankel matrices and operators by means of Vandermonde matrices. In fact, it turns out that these concepts are essentially equivalent.