We propose an algebraic framework generalizing several variants of Prony's method and explaining their relations. This includes Hankel and Toeplitz variants of Prony's method for multivariate exponential sums, sparse polynomials, Gau{\ss}ian sums, spherical harmonic sums, taking also into account whether they have their support on an algebraic set.

中文翻译：

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使用 Prony 结构学习代数分解

我们提出了一个代数框架，概括了 Prony 方法的几种变体并解释了它们的关系。这包括用于多元指数和、稀疏多项式、Gau{\ss}ian 和、球谐和的 Prony 方法的 Hankel 和 Toeplitz 变体，还考虑了它们是否支持代数集。