Prony's method under an almost sharp multivariate Ingham inequality
Abstract
The parameter reconstruction problem in a sum of Dirac measures from its low frequency trigonometric moments is well understood in the univariate case and has a sharp transition of identifiability with respect to the ratio of the separation distance of the parameters and the order of moments. Towards a similar statement in the multivariate case, we present an Ingham inequality which improves the previously best known dimension-dependent constant from square-root growth to a logarithmic one. Secondly, we refine an argument that an Ingham inequality implies identifiability in multivariate Prony methods to the case of commonly used max-degree by a short linear algebra argument, closely related to a flat extension principle and the stagnation of a generalized Hilbert function.
Cite
@article{arxiv.1705.11017,
title = {Prony's method under an almost sharp multivariate Ingham inequality},
author = {Stefan Kunis and H. Michael Möller and Thomas Peter and Ulrich von der Ohe},
journal= {arXiv preprint arXiv:1705.11017},
year = {2017}
}