Prony’s method on the sphere
Kunis, Stefan1 ; Möller, H. Michael2 ; von der Ohe, Ulrich3
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, Tome 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.

Publié le :
DOI : 10.5802/smai-jcm.53
Classification : 65T40, 42C15, 30E05, 65F30
Mots clés : frequency analysis, spectral analysis, exponential sum, moment problem, super-resolution
Kunis, Stefan 1 ; Möller, H. Michael 2 ; von der Ohe, Ulrich 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 
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     title = {Prony{\textquoteright}s method on the sphere},
     journal = {The SMAI Journal of computational mathematics},
     pages = {87--97},
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Kunis, Stefan; Möller, H. Michael; von der Ohe, Ulrich. Prony’s method on the sphere. The SMAI Journal of computational mathematics, Tome S5 (2019), pp. 87-97. doi : 10.5802/smai-jcm.53. http://www.numdam.org/articles/10.5802/smai-jcm.53/

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