46 citations · 413 across the 115 of their papers we have counts for
9 papers · 1 filter
Size of orthogonal sets of exponentials for the disk
Alex Iosevich, Mihail N. Kolountzakis
Suppose $Λ\subseteq \RR^2$ has the property that any two exponentials with frequency from are orthogonal in the space , where $D \subseteq \RR^2$ is the unit disk. Such…
On the Mattila-Sjolin theorem for distance sets
Alex Iosevich, Mihalis Mourgoglou, Krystal Taylor
We extend a result, due to Mattila and Sjolin, which says that if the Hausdorff dimension of a compact set , , is greater than , then…
On angles determined by fractal subsets of the Euclidean space via Sobolev bounds for bi-linear operators
Alex Iosevich, Mihalis Mourgoglou, Eyvindur Palsson
We prove that if the Hausdorff dimension of a compact subset of is greater than , then the set of angles determined by triples of points from this se…
On volumes determined by subsets of Euclidean space
Allan Greenleaf, Alex Iosevich, Mihalis Mourgoglou
Given , define the \emph{volume set} of , . In , we prove that has positive…
Periodicity of the spectrum in dimension one
Alex Iosevich, Mihail N. Kolountzakis
A bounded measurable set , of Lebesgue measure 1, in the real line is called spectral if there is a set of real numbers ("frequencies") such that the exponential functions $…
Multi-parameter projection theorems with applications to sums-products and finite point configurations in the Euclidean setting
B. Erdoğan, D. Hart, A. Iosevich
In this paper we study multi-parameter projection theorems for fractal sets. With the help of these estimates, we recover results about the size of , where…