bibkey: kunis2015multivariateprony authors: Stefan Kunis; Thomas Peter; Tim Roemer; Ulrich von der Ohe year: 2015 title: “A multivariate generalization of Prony’s method” doi: null url: https://arxiv.org/abs/1506.00450v1 claim: “Finite multivariate exponential sums admit polynomial moment and node-separation formulations; quantitative conditioning depends on node separation and coefficient ratios.” strata_touched: [] license: citation-only triage: anchor

Multivariate finite-spectrum interpolation

The cited primary record is arXiv:1506.00450v1. Section 2 defines multivariate exponential sums and the associated polynomial evaluation and moment matrices. Theorem 3.1 uses finite point ideals for exact recovery; Definition 3.6 and Theorem 3.7 record separation and coefficient dependence in conditioning estimates.

The LocalClock application uses this as a consumed interpolation precedent and states its own elementary total-degree bound for phase pairs. That bound is sufficient exact uniqueness for a separate unknown-frequency target; it is not attributed verbatim to this paper, is not a minimum, and gives no uniform finite-precision guarantee for the calibrated known-occupancy fibre.