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Prony's method on the sphere

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.

preprint2016arXivOpen access
Stefan KunisH. Michael MöllerUlrich von der Ohe
math.AGmath.NA
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Stefan KunisH. Michael MöllerUlrich von der Ohe

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