110 citations · 1.9k across the 140 of their papers we have counts for
26 papers · 1 filter
Pure point measures with sparse support and sparse Fourier--Bohr support
Michael Baake, Nicolae Strungaru, Venta Terauds
Fourier-transformable Radon measures are called doubly sparse when both the measure and its transform are pure point measures with sparse support. Their structure is reasonably wel…
Fourier transform of Rauzy fractals and point spectrum of 1D Pisot inflation tilings
Michael Baake, Uwe Grimm
Primitive inflation tilings of the real line with finitely many tiles of natural length and a Pisot--Vijayaraghavan unit as inflation factor are considered. We present an approach…
Scaling of diffraction intensities near the origin: Some rigorous results
Michael Baake, Uwe Grimm
The scaling behaviour of the diffraction intensity near the origin is investigated for (partially) ordered systems, with an emphasis on illustrative, rigorous results. This is an e…
Geometric enumeration problems for lattices and embedded -modules
Michael Baake, Peter Zeiner
In this review, we count and classify certain sublattices of a given lattice, as motivated by crystallography. We use methods from algebra and algebraic number theory to find and e…
Pair correlations of aperiodic inflation rules via renormalisation: Some interesting examples
Michael Baake, Franz Gaehler
This article presents, in an illustrative fashion, a first step towards an extension of the spectral theory of constant length substitutions. Our starting point is the general obse…
On the notions of symmetry and aperiodicity for Delone sets
Michael Baake, Uwe Grimm
Non-periodic systems have become more important in recent years, both theoretically and practically. Their description via Delone sets requires the extension of many standard conce…