This paper is devoted to the decomposition of vectors into sampled complex exponentials; or, equivalently, to the information over discrete measures captured in a finite sequence of their Fourier coefficients. We study existence, uniqueness, and cardinality properties, as well as computational aspects of estimation using convex semidefinite programs. We then explore optimal transport between measures, of which only a finite sequence of Fourier coefficients is known.

中文翻译：

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原子范数最小化以分解为复杂指数并在Fourier域中实现最佳输运

本文致力于将向量分解为采样的复杂指数。或等价地获得以傅立叶系数的有限序列捕获的离散量度的信息。我们研究存在性，唯一性和基数属性，以及使用凸半定程序进行估计的计算方面。然后，我们探索度量之间的最佳传输，其中只有有限序列的傅里叶系数是已知的。