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Prony’s method on the sphere
Stefan Kunis1; H. Michael Möller2; Ulrich von der Ohe3
1 Osnabrück University, Institute of Mathematics and Research Center of Cellular Nanoanalytics, Germany
2 TU Dortmund, Fakultät für Mathematik, Germany
3 University of Genova, Department of Mathematics, Italy; Marie Skłodowska-Curie fellow of the Istituto Nazionale di Alta Matematica
The SMAI Journal of computational mathematics, Volume S5 (2019), pp. 87-97.

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 in the nonnegative case.

Published online:
DOI: 10.5802/smai-jcm.53
Classification: 65T40, 42C15, 30E05, 65F30
Keywords: frequency analysis, spectral analysis, exponential sum, moment problem, super-resolution

Stefan Kunis 1; H. Michael Möller 2; Ulrich von der Ohe 3

1 Osnabrück University, Institute of Mathematics and Research Center of Cellular Nanoanalytics, Germany
2 TU Dortmund, Fakultät für Mathematik, Germany
3 University of Genova, Department of Mathematics, Italy; Marie Skłodowska-Curie fellow of the Istituto Nazionale di Alta Matematica
License: CC-BY-NC-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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     title = {Prony{\textquoteright}s method on the sphere},
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Stefan Kunis; H. Michael Möller; Ulrich von der Ohe. Prony’s method on the sphere. The SMAI Journal of computational mathematics, Volume S5 (2019), pp. 87-97. doi : 10.5802/smai-jcm.53. https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.53/

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