12 papers
Uncertainty Principles, Spectral Localization, and Singular Schrödinger Operators on Compact Manifolds
Alex Iosevich, Chamsol Park
We establish uncertainty principles on compact Riemannian manifolds without boundary by combining restriction estimates for orthonormal systems with spectral projection bounds for…
High-Dimensional Signal Compression: Lattice Point Bounds and Metric Entropy
A. Iosevich, A. Vagharshakyan, E. Wyman
We study worst-case signal compression under an energy constraint, with coordinate-dependent quantization precisions. The compression problem is reduced to counting lattic…
Spectral synthesis with the complexity parameter
S. Deodhar, A. Iosevich
We show that spectral synthesis thresholds are governed by a quantitative spectral complexity parameter, the Fourier Ratio, in addition to the geometric size of the Fourier support…
Spectral synthesis on Riemannian manifolds
A. Iosevich, A. Mayeli, E. Wyman
We study spectral synthesis for measures supported on thin subsets of compact Riemannian manifolds. We prove that under natural non-concentration conditions, such measures admit qu…
Discretization, sampling, and the Fourier ratio
A. Iosevich, E. Palsson, A. Yavicoli
We derive fundamental sampling bounds for smooth signals in continuous settings without sparsity assumptions. By introducing the Fourier ratio as a measure of spectral compressibil…
The Fourier Ratio: A Unifying Measure of Complexity for Recovery, Localization, and Learning
Will Burstein, Alex Iosevich, Hari Sarang Nathan
We introduce a generalized Fourier ratio, the \(\ell^1/\ell^2\) norm ratio of coefficients in an \emph{arbitrary} orthonormal system, as a single, basis-invariant measure of \emph{…
The Fourier Ratio and complexity of signals
K. Aldaleh, W. Burstein, G. Garza +12
We study the Fourier ratio of a signal , \[ \mathrm{FR}(f)\ :=\ \sqrt{N}\,\frac{\|\widehat f\|_{L^1(μ)}}{\|\widehat f\|_{L^2(μ)}} \ =\ \frac{\|\widehat f…
Orlicz spaces and the uncertainty principle
A. Iosevich, I. Li, Z. Li +1
Let be a finite signal. The classical uncertainty principle tells us that the product of the support of and the support of , the Fourier transform of , must sat…
On spectral synthesis in
P. Bhowmik, S. Deodhar, A. Iosevich
A classical result due to Agranovsky and Narayanan (\cite{AN04}) says that if the support of the Fourier transform of is carried by a smooth meas…
Fourier minimization and imputation of time series
Will Burstein, Alex Iosevich, Azita Mayeli +1
One of the most common procedures in modern data analytics is filling in missing values in times series. For a variety of reasons, the data provided by clients to obtain a forecast…
Uncertainty Principle, annihilating pairs and Fourier restriction
Philippe Jaming, Alexander Iosevich, Azita Mayeli
Let be a locally compact abelian group, and let denote its dual group, equipped with a Haar measure. A variant of the uncertainty principle states that for any $S…
Effective support, Dirac combs, and signal recovery
G. Garza, K. Gurevich, A. Iosevich +3
Let be a signal with the Fourier transform . A classical result due to Matolcsi and Szucs (\cite{MS73}), and…