7 papers
Additive energy and Fourier complexity of graphs
Vishal Gupta, Sam Ferguson, Alex Iosevich +3
We study the additive energy and the Fourier approximation of graph adjacency matrices labeled by a cyclic group. For a graph with vertices, edges and adjacency matrix ,…
Fuglede's conjecture holds in for and
Samuel J. Ferguson, Joshua Iosevich
Fuglede's conjecture in says that a nonempty set tiles by translation if and only if it is spectral. We prove the conjecture in and $\mathbb{F}_{1…
Edge complexity of graphs
Vishal Gupta, Alex Iosevich, Joshua Iosevich +2
Gupta and Iosevich introduced the edge complexity of a graph as the minimum Fourier ratio of its adjacency matrix over all vertex labelings and bounded it below by graph energy div…
PDE propagation, sampling, and the Fourier ratio
A. Iosevich, J. Iosevich, E. Palsson +1
We study recovery from incomplete random spatial samples for discretized fields arising as fixed-time snapshots of partial differential equations. The organizing parameter is the F…
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…
Refined additive uncertainty principle
Ivan Bortnovskyi, June Duvivier, Alex Iosevich +8
Signal recovery from incomplete or partial frequency information is a fundamental problem in harmonic analysis and applied mathematics, with wide-ranging applications in communicat…
Additive energy, uncertainty principle and signal recovery mechanisms
K. Aldahleh, A. Iosevich, J. Iosevich +3
Given a signal , where is a finite abelian group, under what reasonable assumptions can we guarantee the exact recovery of from a proper subset of its Fou…