A. Iosevich

activity

19992025

most citedThe Fuglede Conjecture holds in

Z_{p} \times Z_{p}

46 citations · 413 across the 115 of their papers we have counts for

collaborators

Showing 2017 · math.CAShow all

10 papers · 2 filters

math.CA2017

On Gabor orthonormal bases over finite prime fields

A. Iosevich, M. Kolountzakis, Yu. Lyubarskii +2

We study Gabor orthonormal windows in $L^{2} (Z_{p}^{d})$ for translation and modulation sets $A$ and $B$ , respectively, where $p$ is prime and $d \geq 2$ . We prove that for a set $…

math.CA2017

Finite field restriction estimates for the paraboloid in high even dimensions

Alex Iosevich, Doowon Koh, Mark Lewko

We prove that the finite field Fourier extension operator for the paraboloid is bounded from $L^{2} \to L^{r}$ for $r \geq \frac{2 d + 4}{d}$ in even dimensions $d \geq 8$ , which is the optim…

math.CA2017

On the unit distance problem

Alex Iosevich

The Erd\H os unit distance conjecture in the plane says that the number of pairs of points from a point set of size $n$ separated by a fixed (Euclidean) distance is $\leq C_ε n^{1+…

math.CA2017★ 6 cited

Rigidity, graphs and Hausdorff dimension

N. Chatzikonstantinou, A. Iosevich, S. Mkrtchyan +1

For a compact set $E \subset R^{d}$ and a connected graph $G$ on $k + 1$ vertices, we define a $G$ -framework to be a collection of $k + 1$ points in $E$ such that the distance be…

math.CA2017★ 2 cited

Gabor orthogonal bases and convexity

Alex Iosevich, Azita Mayeli

Let $g (x) = χ_{B} (x)$ be the indicator function of a bounded convex set in $R^{d}$ , $d \geq 2$ , with a smooth boundary and everywhere non-vanishing Gaussian curvature. Using a combin…

math.CA2017★ 6 cited

Pinned distance problem, slicing measures and local smoothing estimates

Alex Iosevich, Bochen Liu

We improve the Peres-Schlag result on pinned distances in sets of a given Hausdorff dimension. In particular, for Euclidean distances, with $Δ^{y} (E) = {∣ x - y ∣ : x \in E},$ we prove…