Prony's method on the sphere
Autor(en): | Kunis, S. Möller, H.M. von der Ohe, U. |
Stichwörter: | exponential sum; frequency analysis; moment problem; spectral analysis; super-resolution | Erscheinungsdatum: | 2019 | Herausgeber: | Centre Mersenne | Journal: | SMAI Journal of Computational Mathematics | Volumen: | S5 | Startseite: | 87 | Seitenende: | 97 | Zusammenfassung: | 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. © Société de Mathématiques Appliquées et Industrielles, 2019 Certains droits réservés. |
ISSN: | 2426-8399 | DOI: | 10.5802/smai-jcm.53 | Externe URL: | https://www.scopus.com/inward/record.uri?eid=2-s2.0-85083381897&doi=10.5802%2fsmai-jcm.53&partnerID=40&md5=91a1062d77cf35f4e8a7daf003a87e1c |
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geprüft am 17.05.2024