Related papers: Why do Meyer sets diffract?
We study dynamical systems $(X,G,m)$ with a compact metric space $X$ and a locally compact, $\sigma$-compact, abelian group $G$. We show that such a system has discrete spectrum if and only if a certain space average over the metric is a…
Beyond classical Bragg diffraction, we report on new sub-Bragg phenomena to achieve enhanced sound wave tunability in the low-frequency range in a multilayered acoustic metamaterial system. Remarkably, we reveal and study the formation of…
We first recall some basic definitions and facts about Jacobi manifolds, generalized Lie bialgebroids, generalized Courant algebroids and Dirac structures. We establish an one-one correspondence between reducible Dirac structures of the…
We investigate the reproducing properties of Gabor systems within the context of expansible groups. These properties are established in terms of density conditions. The concept of density that we employ mirrors the well-known Beurling…
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 measure with continuous diffraction spectra is zero. In…
Diffraction is a fundamental property of light propagation. Owing to this phenomenon,light diffracts out in all directions when it passes through a subwavelength slit.This imposes a fundamental limit on the transverse size of a light beam…
We analyze the properties of weakly compact sets in Lipschitz free spaces. Prior research has established that, for a complete metric space $M$, weakly precompact sets in the Lipschitz free space $\mathcal F(M)$ are tight. In this paper, we…
A discrete set $A$ in the Euclidian space is almost periodic if the measure with the unite masses at points of the set is almost periodic in the weak sense. We investigate properties of such sets in the case when $A-A$ is discrete. In…
We analyze the canonical treatment of classical constrained mechanical systems formulated with a discrete time. We prove that under very general conditions, it is possible to introduce nonsingular canonical transformations that preserve the…
It is shown that there exists a normal uniform algebra, on a compact metrizable space, that fails to be strongly regular at some peak point. This answers a 31-year-old question of Joel Feinstein. Our example is R(K) for a certain compact…
Most of the examples of wavelet sets are for dilation sets which are groups. We find a necessary and sufficient condition under which subspace wavelet sets exist for dilation sets of the form $A B$, which are not necessarily groups. We…
We construct two connected plane sets which can be embedded into rational curves. The first is a biconnected set with a dispersion point. It answers a question of Joachim Grispolakis. The second is indecomposable. Both examples are…
We establish an exponential error term for the renewal theorem in the context of products of random matrices, which is surprising compared with classical abelian cases. A key tool is the Fourier decay of the Furstenberg measures on the…
We give necessary and sufficient conditions for a regular semi-Dirichlet form to enjoy a new Feller type property, which we call \emph{weak Feller property}. Our characterization involves potential theoretic as well as probabilistic aspects…
This paper considers some open questions related to the inverse problem of pure point diffraction, in particular, what types of objects may diffract, and which of these may exhibit the same diffraction. Some diverse objects with the same…
We define a new diffusive matrix model converging towards the $\beta$ -Dyson Brownian motion for all $\beta\in [0,2]$ that provides an explicit construction of $\beta$-ensembles of random matrices that is invariant under the…
To prove that a measure, linearly representable by means of a finite set of nonnegative matrices $\mathcal M$, has the weak-Gibbs property, one check the uniform convergence (on $\mathcal M^\mathbb N$) of the sequence of vectors…
We continue our study, initiated in our earlier paper, of Riemann surfaces with constant curvature and isolated conic singularities. Using the machinery developed in that earlier paper of extended configuration families of simple divisors,…
We prove a general result on irregularities of distribution for Borel sets intersected with bounded measurable sets or affine half-spaces.
Cut and project sets are obtained by taking an irrational slice of a lattice and projecting it to a lower dimensional subspace, and are fully characterised by the shape of the slice (window) and the choice of the lattice. In this context we…