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math.CA2026
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…
math.CA2025
The Fourier Ratio: Uncertainty, Restriction, and Approximation for Compactly Supported Measures
A. Iosevich, Z. Li, E. Palsson +1
We introduce a continuous analog of the Fourier ratio for compactly supported Borel measures. For a measure \(μ\) on \(\mathbb{R}^d\) and \(f\in L^2(μ)\), the Fourier ratio compare…
math.CA2024
Packing sets in Euclidean space by affine transformations
Alex Iosevich, Pertti Mattila, Eyvindur Palsson +4
For Borel subsets (the set of all rigid motions) and , we define \begin{align*} Θ(E):=\bigcup_{(g,z)\in Θ}(gE+z). \end{ali…