41 citations · 310 across the 48 of their papers we have counts for
53 papers
Eberlein convolution as an inner product and quantitative Bombieri--Taylor results
Daniel Lenz, Nicolae Strungaru
We present a simple argument providing a very general Bombieri--Taylor-type result to compute Bragg peaks in diffraction theory as limits. At its abstract core the argument relies…
Pseudorandomness and Diffraction
David Damanik, Nicolae Strungaru
Pseudorandom structures are structures that behave like random ones, without necessarily being random themselves. It is a prominent, and evidently very difficult, conjecture that $…
Continuous diffraction spectrum and the uniform vanishing of Fourier--Bohr coefficients
Nicolae Strungaru
In this paper we review the connection among continuity of the diffraction spectrum, the (uniform) vanishing of the Fourier--Bohr coefficients and the so called consistent phase fr…
On almost periodicity in crystalline measures
Jan Mazáč, Christoph Richard, Nicolae Strungaru
Meyer defined crystalline measures as tempered distributions such that both and its Fourier transform are pure-point Radon measures of locally finite support. H…
The 1-2-3 conjecture for polygonal tilings
Alison Charlesworth, Christopher Ramsey, Nicolae Strungaru
The 1-2-3 conjecture has been solved positively in 2024 for finite graphs and by extension for infinite graphs which are locally finite. The solution is non-constructive, and findi…
On the spectrum of non-ergodic measures
Michael Francis, Christopher Ramsey, Nicolae Strungaru
Consider a topological dynamical system where the group is abelian and the topologies are locally compact and second-countable. Given an invariant measure for this system, we show…
Wiener--Wintner points for topological dynamical systems
Daniel Lenz, Nicolae Strungaru
We consider measurable and topological dynamical systems over locally compact abelian groups. Our main observation relates convergence of Wiener-Wintner type averages to eigenvalue…
Twice Fourier transformable measures and diffraction theory
Hans G. Feichtinger, Christoph Richard, Christoph Schumacher +1
Mathematical diffraction theory has been developed since about 1995. Hof's initial approach relied on tempered distributions in euclidean space. Nowadays often the Fourier theory b…
Which Meyer sets are regular model sets? A characterization via almost periodicity
Daniel Lenz, Christoph Richard, Nicolae Strungaru
In 2012, Meyer introduced the notions of generalized almost periodic measure and almost periodic pattern and proved that regular model sets in Euclidean space are almost periodic p…
Relative position in binary substitutions
Michael Coons, Christopher Ramsey, Nicolae Strungaru
Given an infinite word on a finite alphabet, an immediate question arises:~can we understand the frequency of letters in \,? For words that are the fixed points…
Diffraction of the primes and other sets of zero density
Adam Humeniuk, Christopher Ramsey, Nicolae Strungaru
In this paper, we show that the diffraction of the primes is absolutely continuous, showing no bright spots (Bragg peaks). We introduce the notion of counting diffraction, extendin…
Circles in diffraction
Emily R. Korfanty, Nicolae Strungaru
Given a Fourier transformable measure in two dimensions, we find a formula for the intensity of its Fourier transform along circles. In particular, we obtain a formula for the diff…
Diffraction as a unitary representation and the orthogonality of measures with respect to the reflected Eberlein convolution
Daniel Lenz, Nicolae Strungaru
We discuss how the diffraction theory of a single translation bounded measure or a family of such measures can be understood within the framework of unitary group representations.…
Pure point diffraction and almost periodicity
Daniel Lenz, Timo Spindeler, Nicolae Strungaru
This article deals with pure point diffraction and its connection to various notions of almost periodicity. We explain why the Fibonacci chain does not fit into the classical class…
Generating functions of substitutions
Aisling Pouti, Christopher Ramsey, Nicolae Strungaru
In this paper we study substitutions and some of their associated generating functions. This association takes aperiodicity to transcendence, and vice-versa. These generating funct…
The (twisted) Eberlein convolution of measures
Daniel Lenz, Timo Spindeler, Nicolae Strungaru
In this paper, we study the properties of the Eberlein convolution of measures and introduce a twisted version of it. For functions we show that the twisted Eberlein convolution ca…
Inter model sets in are model sets
Christoph Richard, Nicolae Strungaru
We show that any translate of a model set is a model set in some modified cut-and-project scheme. Restricting to Euclidean direct space, we show that any translate of an inter mode…
Colourings of aperiodic tilings
Molly Evans, Dylan Gawlak, Christopher Ramsey +2
We find explicit optimal vertex, edge and face coulourings for the chair tiling, the Ammann--Beenker tiling, the rational pinwheel tiling and the pinwheel tiling.
Abstract almost periodicity for group actions on uniform topological spaces
Daniel Lenz, Timo Spindeler, Nicolae Strungaru
We present a unified theory for the almost periodicity of functions with values in an arbitrary Banach space, measures and distributions via almost periodic elements for the action…
A note on tempered measures
Michael Baake, Nicolae Strungaru
The relation between tempered distributions and measures is analysed and clarified. While this is straightforward for positive measures, it is surprisingly subtle for signed or com…
Fourier Transformable Measures with Meyer set support and their lift to the cut and project scheme
Nicolae Strungaru
In this paper, we prove that given a cut-and-project scheme and a compact window , the natural projection gives a bijection between the Fourier…
Semi-measures and their Fourier transform
Timo Spindeler, Nicolae Strungaru
The basic theory of semi-measures on locally compact Abelian groups is extended to prove the existence of a generalised Eberlein decomposition into such semi-measures.
On the orthogonality of measures of different spectral type with respect to twisted Eberlein convolution
Nicolae Strungaru
In this paper we show that under suitable conditions on their Fourier--Bohr coefficients, the twisted Eberlein convolution of a measure with pure point diffraction spectra and a me…
Spectrum of weak model sets with Borel windows
Gerhard Keller, Christoph Richard, Nicolae Strungaru
Consider the extended hull of a weak model set together with its natural shift action. Equip the extended hull with the Mirsky measure, which is a certain natural pattern frequency…