151 citations · 167 across the 9 of their papers we have counts for
14 papers · 1 filter
The discrepancy of a needle on a checkerboard
Mihail N. Kolountzakis
Consider the plane as a checkerboard, with each unit square colored black or white in an arbitrary manner. We show that for any such coloring there are straight line segments, of a…
Covering the plane by rotations of a lattice arrangement of disks
Alex Iosevich, Mihail N. Kolountzakis, Mate Matolcsi
Suppose we put an -disk around each lattice point in the plane, and then we rotate this object around the origin for a set of angles. When do we cover the whole plane, excep…
Complex Hadamard matrices and the Spectral Set Conjecture
Mihail N. Kolountzakis, Mate Matolcsi
By analyzing the connection between complex Hadamard matrices and spectral sets we prove the direction ``spectral -> tile'' of the Sectral Set Conjecture for all sets A of size at…
Tiles with no spectra
Mihail N. Kolountzakis, Mate Matolcsi
We exhibit a subset of a finite Abelian group, which tiles the group by translation, and such that its tiling complements do not have a common spectrum (orthogonal basis for their…
Turán's extremal problem for positive definite functions on groups
Mihail N. Kolountzakis, Szilard Gy. Revesz
We study the following question: Given an open set , symmetric about 0, and a continuous, integrable, positive definite function , supported in and with , how lar…
A Weyl type formula for Fourier spectra and frames
Alex Iosevich, Mihail N. Kolountzakis
We prove qualitative and quantitative results concerning the asymptotic density in dilates of centered convex bodies of the frequency vectors of orthogonal exponential bases and fr…