BDBenedikt Diederichs
Benedikt Diederichs
*This is an algorithmically generated author record based on publicly available information.
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Benedikt Diederichs has a total of 2 co-authors. Here are the top co-authors by number of shared publications:
- Effie Papageorgiou
Institut fur Mathematik, Universitat Paderborn, Paderborn, Germany
2 shared publications - Mihail N. Kolountzakis
Department of Mathematics and Applied Mathematics, University of Crete, Heraklion, Greece
2 shared publications
Latest Publications
- Open Access
- 21 October 2022
- Published by Springer Nature in Monatshefte für Mathematik
- Vol. 200 (1) , 23-42
How many Fourier coefficients are needed?
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 $$0, 1, \ldots , N$$ are sufficient to determine the function (the intervals). In the second case we produce a set of locations of size $$O(N \log ^{d-1} N)$$ which suffices to determine the measure.- 21 October 2022
- Published by Springer Nature in Monatshefte für Mathematik
- Vol. 200 (1) , 23-42
Open AccessHow many Fourier coefficients are needed?
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 $$0, 1, \ldots , N$$ are sufficient to determine the function (the intervals). In the second case we produce a set of locations of size $$O(N \log ^{d-1} N)$$ which suffices to determine the measure. - Open Access
How many Fourier coefficients are needed?
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 $0, 1, \ldots, N$ are sufficient to determine the function (the intervals). In the second case we produce a set of locations of size $O(N \log^{d-1} N)$ which suffices to determine the measure.Open AccessHow many Fourier coefficients are needed?
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 $0, 1, \ldots, N$ are sufficient to determine the function (the intervals). In the second case we produce a set of locations of size $O(N \log^{d-1} N)$ which suffices to determine the measure.