10 papers · 1 filter
Minkowski sums with convex curves without pointwise Fourier decay
Alex Iosevich, Zhangze Li, Eyvindur Palsson +2
Let be a compact convex graph and define \[ T(Γ) = \inf \left\{ t: \dim_{\mathrm H}(E)>t \Longrightarrow |E+Γ|>0 \text{ for every compact }E\subset\mathbb R^2…
Arithmetic-progression gap sets in Cantor sets
Samantha Sandberg-Clark, Krystal Taylor, Alexia Yavicoli
We address the question of which common differences can arise in arithmetic progressions contained in fractal sets. For a compact set , we investigate not only w…
The Erdős Similarity Conjecture for Two-Fold Sumsets with a Geometric Summand
N. Mora Cuellar, A. Iosevich, N. Kulkarni +2
We settle a major case in the two-set regime of the Erdős similarity conjecture: the sum of a geometric sequence and an arbitrary infinite set is never measure universal. Here a se…
Falconer lattice sets and the Erdos similarity problem
A. Iosevich, A. Yavicoli
We show that a family of extremely thin sets satisfy the Erdős similarity conjecture. These examples lie outside the range covered by recent work of Shmerkin and Yavicoli \cite{Shm…
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 compare…