2 citations · 3 across the 6 of their papers we have counts for
7 papers
Bounded remainder sets, bounded distance equivalent cut-and-project sets, and equidecomposability
Mark Mordechai Etkind, Sigrid Grepstad, Mihail N. Kolountzakis +1
We use the measurable Hall's theorem due to Cieśla and Sabok to prove that (i) if two measurable sets of the same measure are bounded remainder sets with…
The Turán and Delsarte problems and their duals
Mihail N. Kolountzakis, Nir Lev, Máté Matolcsi
We study two optimization problems for positive definite functions on Euclidean space with restrictions on their support and sign: the Turan problem and the Delsarte problem. These…
Fuglede's conjecture on orthogonal bases of exponentials
Mihail N. Kolountzakis
We discuss part of Fuglede's original paper (1974) in which he posed his famous conjecture on which bodies in Euclidean space admit an orthogonal basis of exponentials for their $L…
Geometric implications of weak tiling
Mihail N. Kolountzakis, Nir Lev, Máté Matolcsi
The notion of weak tiling played a key role in the proof of Fuglede's spectral set conjecture for convex domains, due to the fact that every spectral set must weakly tile its compl…
Maximality and completeness of orthogonal exponentials on the cube
Mihail N. Kolountzakis, Nir Lev, Máté Matolcsi
It is possible to have a packing by translates of a cube that is maximal (i.e.\ no other cube can be added without overlapping) but does not form a tiling. In the long running anal…
Orthogonal Fourier Analysis on Domains
Mihail N. Kolountzakis
In this paper we go over the history of the Fuglede or Spectral Set Conjecture as it has developed over the last 30 years or so. We do not aim to be exhaustive and we do not cover…