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arXiv · 1603.02020

Prony's method on the sphere

Stefan Kunis·H. Michael Möller·Ulrich von der Ohe
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Abstract

Eigenvalue analysis based methods are well suited for the reconstruction of finitely supported measures from their moments up to a certain degree. We give a precise description when Prony's method succeeds in terms of an interpolation condition. In particular, this allows for the unique reconstruction of a measure from its trigonometric moments whenever its support is separated and also for the reconstruction of a measure on the unit sphere from its moments with respect to spherical harmonics. Both results hold in arbitrary dimensions and also yield a certificate for popular semidefinite relaxations of these reconstruction problems.

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Stefan Kunis, H. Michael Möller, Ulrich von der Ohe. 2016-03-07. Prony's method on the sphere. https://arxiv.org/abs/1603.02020

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