10 papers
Arithmetic-progression gap sets in Cantor sets
Samantha Sandberg, Samantha Sandberg-Clark, Krystal Taylor +1
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…
Additive and multiplicative densities, prime valuations and symbolic models
Natalia Mora Cuellar, Ignacio Rojas Aravena, Alexia Yavicoli
We study additive and multiplicative densities of subsets of along prescribed Følner sequences. We prove that additive upper density one implies multiplicative density one al…
The ErdÅs 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 ErdÅs similarity conjecture: the sum of a geometric sequence and an arbitrary infinite set is never measure universal. Here a s…
Falconer lattice sets and the Erdos similarity problem
A. Iosevich, A. Yavicoli
We show that a family of extremely thin sets satisfy the ErdÅs similarity conjecture. These examples lie outside the range covered by recent work of Shmerkin and Yavicoli \cite{Sh…
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…
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…