PuSH - Publikationsserver des Helmholtz Zentrums München

Diederichs, B. ; Kolountzakis, M.N.* ; Papageorgiou, E.*

How many Fourier coefficients are needed?

Monatsh. Math. 200, 23–42 (2023)
Verlagsversion DOI
Open Access Gold (Paid Option)
Creative Commons Lizenzvertrag
We are looking at families of functions or measures on the torus which are specified by a finite number of parameters N. The task, for a given family, is to look at a small number of Fourier coefficients of the object, at a set of locations that is predetermined and may depend only on N, and determine the object. We look at (a) the indicator functions of at most N intervals of the torus and (b) at sums of at most N complex point masses on the multidimensional torus. In the first case we reprove a theorem of Courtney which says that the Fourier coefficients at the locations 0 , 1 , … , N are sufficient to determine the function (the intervals). In the second case we produce a set of locations of size O(Nlog d-1N) which suffices to determine the measure.
Weitere Metriken?
Zusatzinfos bearbeiten [➜Einloggen]
Publikationstyp Artikel: Journalartikel
Dokumenttyp Wissenschaftlicher Artikel
Schlagwörter Fourier Coefficients ; Interpolation ; Inverse Problem ; Non-harmonic Exponential Sums ; Sparse Exponential Sums
ISSN (print) / ISBN 0026-9255
Quellenangaben Band: 200, Heft: , Seiten: 23–42 Artikelnummer: , Supplement: ,
Verlag Universität Wien
Begutachtungsstatus Peer reviewed
Förderungen Hellenic Foundation for Research and Innovation
University of Crete