Home
Deutsch
Advanced Search
Browse by ...
Publication overview
Contact persons
Help
Publ. Version/Full Text
DOI
 |
Open Access Gold (Paid Option) |
|
as soon as is submitted to ZB.
How many Fourier coefficients are needed?
Monatsh. Math. 200, 23–42 (2023)
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.
Altmetric
Additional Metrics?
Edit extra informations
Login
Publication type
Article: Journal article
Document type
Scientific Article
Keywords
Fourier Coefficients ; Interpolation ; Inverse Problem ; Non-harmonic Exponential Sums ; Sparse Exponential Sums
ISSN (print) / ISBN
0026-9255
Journal
Monatshefte für Mathematik
Quellenangaben
Volume: 200,
Pages: 23–42
Publisher
Universität Wien
Non-patent literature
Publications
Reviewing status
Peer reviewed
Institute(s)
Institute of Biological and Medical Imaging (IBMI)
Grants
Hellenic Foundation for Research and Innovation
University of Crete
University of Crete