34 citations · 149 across the 17 of their papers we have counts for
19 papers
Linear independence of time-frequency translates for ultimately positive functions
Romanos Diogenes Malikiosis, Nikos Poursalidis
We prove that the HRT conjecture holds when the Gabor system consists of a 4-point set in the time-frequency plane and a square-integrable function that is ultimately positive. We…
Principal minors of Fourier matrices of square-free order
Andrei Caragea, Dae Gwan Lee, Romanos Malikiosis +1
Chebotarev's theorem on roots of unity states that all minors of a Fourier matrix are non-zero if and only if the order of the matrix is prime. We establish cases in which all prin…
Linearly-exponential checking is enough for the Lonely Runner Conjecture and some of its variants
Romanos Diogenes Malikiosis, Francisco Santos, Matthias Schymura
Tao (2018) showed that in order to prove the Lonely Runner Conjecture (LRC) up to runners it suffices to consider positive integer velocities in the order of . Us…
A linear programming approach to Fuglede's conjecture in
Romanos Diogenes Malikiosis
We present an approach to Fuglede's conjecture in using linear programming bounds, obtaining the following partial result: if with $p^2-…
Fuglede's conjecture holds for cyclic groups of order
Gergely Kiss, Romanos Diogenes Malikiosis, Gábor Somlai +1
The tile-spectral direction of the discrete Fuglede-conjecture is well-known for cyclic groups of square-free order, initiated by Laba and Meyerowitz, but the spectral-tile directi…
Computing the covering radius of a polytope with an application to lonely runners
Jana Cslovjecsek, Romanos Diogenes Malikiosis, Márton Naszódi +1
We are concerned with the computational problem of determining the covering radius of a rational polytope. This parameter is defined as the minimal dilation factor that is needed f…
On the structure of spectral and tiling subsets of cyclic groups
Romanos Diogenes Malikiosis
The purpose of this paper is to investigate the properties of spectral and tiling subsets of cyclic groups, with an eye towards the spectral set conjecture in one dimension, which…
Full Spark Frames in the Orbit of a Representation
Romanos Diogenes Malikiosis, Vignon Oussa
We present a new infinite family of full spark frames in finite dimensions arising from a unitary group representation, where the underlying group is the semi-direct product of a c…
On the discrete Fuglede and Pompeiu problems
Gergely Kiss, Romanos Diogenes Malikiosis, Gábor Somlai +1
We investigate the discrete Fuglede's conjecture and Pompeiu problem on finite abelian groups and develop a strong connection between the two problems. We give a geometric conditio…
Formal duality in finite cyclic groups
Romanos Diogenes Malikiosis
The notion of formal duality in finite Abelian groups appeared recently in relation to spherical designs, tight sphere packings, and energy minimizing configurations in Euclidean s…
Fuglede's conjecture on cyclic groups of order
Romanos-Diogenes Malikiosis, Mihail N. Kolountzakis
We show that the spectral set conjecture by Fuglede holds in the setting of cyclic groups of order , where , are distinct primes and . This means that a subse…
On the covering radius of lattice zonotopes and its relation to view-obstructions and the lonely runner conjecture
Matthias Henze, Romanos-Diogenes Malikiosis
The goal of this paper is twofold; first, show the equivalence between certain problems in geometry, such as view-obstruction and billiard ball motions, with the estimation of cove…
Spark deficient Gabor frames
Romanos-Diogenes Malikiosis
The theory of Gabor frames of functions defined on finite abelian groups was initially developed in order to better understand the properties of Gabor frames of functions defined o…
Rotations by roots of unity and Diophantine approximation
Romanos-Diogenes Malikiosis
For a fixed integer , we study the question whether at least one of the numbers , , is -close to an integer, for any possible value of $X\i…
Polyhedral Gauss Sums, and polytopes with symmetry
Romanos-Diogenes Malikiosis, Sinai Robins, Yichi Zhang
We define certain natural finite sums of 'th roots of unity, called , that are associated to each convex integer polytope , and which generalize the classical -dim…
A note on Gabor frames in finite dimensions
Romanos-Diogenes Malikiosis
The purpose of this note is to present a proof of the existence of Gabor frames in general linear position in all finite dimensions. The tools developed in this note are also helpf…
A note on the pyjama problem
R. D. Malikiosis, M. Matolcsi, I. Z. Ruzsa
This note concerns the so-called pyjama problem, whether it is possible to cover the plane by finitely many rotations of vertical strips of half-width . We first prove…
Lattice-point enumerators of ellipsoids
Romanos-Diogenes Malikiosis
Minkowski's second theorem on successive minima asserts that the volume of a 0-symmetric convex body K over the covolume of a lattice Λcan be bounded above by a quantity involving…
A discrete analogue for Minkowski's second theorem on successive minima
Romanos Malikiosis
The main result of this paper is an inequality relating the lattice point enumerator of a 3-dimensional, 0-symmetric convex body and its successive minima. This is an example of ge…