Prony's Method Under an Almost Sharp Multivariate Ingham Inequality
Autor(en): | Kunis, Stefan Moeller, H. Michael Peter, Thomas von der Ohe, Ulrich |
Stichwörter: | 30E05; 42C15; 65F30; 65T40; ALGORITHMS; Exponential sum; EXPONENTIAL-SUMS; FINITE RATE; Frequency analysis; Ingham inequality; INNOVATION; INTERPOLATION; Mathematics; Mathematics, Applied; MAXIMUM-LIKELIHOOD; Moment problem; PARAMETER-ESTIMATION; SIGNALS; SINUSOIDS; Super-resolution; TOTAL LEAST-SQUARES | Erscheinungsdatum: | 2018 | Herausgeber: | SPRINGER BIRKHAUSER | Journal: | JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS | Volumen: | 24 | Ausgabe: | 5 | Startseite: | 1306 | Seitenende: | 1318 | Zusammenfassung: | The parameter reconstruction problem in a sum of Dirac measures from its low frequency trigonometric moments is well understood in the univariate case and has a sharp transition of identifiability with respect to the ratio of the separation distance of the parameters and the order of moments. Towards a similar statement in the multivariate case, we present an Ingham inequality which improves the previously best known dimension-dependent constant from square-root growth to a logarithmic one. Secondly, we refine an argument that an Ingham inequality implies identifiability in multivariate Prony methods to the case of commonly used max-degree by a short linear algebra argument, closely related to a flat extension principle and the stagnation of a generalized Hilbert function. |
ISSN: | 10695869 | DOI: | 10.1007/s00041-017-9571-5 |
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