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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