8 papers
Tilings, packings, and the existence of Schwartz-class Gabor windows
Andrei Caragea, Mihail N. Kolountzakis, Götz Pfander
The existence and construction of Schwartz-class windows for lattice Gabor frames is a central problem in time--frequency analysis. For general time--frequency lattices, we charact…
Spectrality of factors of product spectral measures
Mihail N. Kolountzakis, Chun-Kit Lai, Kailing Lai +1
We refine the method by Greenfeld and Lev for the product spectral set problem and generalize the theorem to a singular measure setting. Furthermore, we establish a new class of sp…
Spectra for finite unions of line segments
Mihail N. Kolountzakis, Ruxi Shi, Sha Wu
In this paper we study the spectrality of arc-length measures supported on the union of two line segments in the plane. We show that any such spectral measure must admit a line spe…
Bounded common fundamental domains for two lattices
Sigrid Grepstad, Mihail N. Kolountzakis
We prove that for any two lattices of the same volume there exists a measurable, bounded, common fundamental domain of them. In other words, there exi…
Exponential polynomials and identification of polygonal regions from Fourier samples
Mihail N. Kolountzakis, Emmanuil Spyridakis
Consider the set of all bivariate exponential polynomials where the polynomials $p_j \in \mathbb{C}[ξ,…
Bounded lattice tiles that pack with another lattice
Sigrid Grepstad, Mihail N. Kolountzakis, Emmanuil Spyridakis
Suppose L and M are full-rank lattices in Euclidean space, such that vol(L) < vol(M). Answering a question of Han and Wang from 2001, we show how to construct a bounded measurable…