From the 1 of 6 linked papers with an AI index.
6 papers
Nonempty interior of pinned distance and tree sets
Tainara Borges, Benjamin Foster, Yumeng Ou +1
The authors establish new dimensional thresholds under which a compact set in the plane has a point whose pinned distance set contains an interval, improving previous results and e…
On volume vectors determined by hypergraphs in thin subsets of Euclidean space
Tainara Borges, Ben Foster, Yumeng Ou +2
Generalizing the Falconer distance problem, the authors of this paper recently established the first non-trivial dimensional threshold for any distance graph in high enough of a di…
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…
Falconer-type results for any finite graph with multiple pins
Tainara Borges, Ben Foster, Yumeng Ou +2
A generalization of the celebrated Falconer distance problem asks for a graph , with vertex set and edge set , how large the…
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: 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 compa…