Related papers: Almost Periodic Measures and Meyer Sets

On the torus group, on the group of p-adic integers and on the p-adic solenoid, we give a construction of an arbitrary weakly infinitely divisible probability measure using a random element with values in a product of (possibly infinitely…

We show that in doubling, geodesic metric measure spaces (including, for example, Euclidean space), sets of positive measure have a certain large-scale metric density property. As an application, we prove that a set of positive measure in…

We develop a unified framework for nonlinear subdivision schemes on complete metric spaces (CMS). We begin with CMS preliminaries and formalize refinement in CMS, retaining key structural properties, such as locality. We prove a convergence…

We study Stepanov and Weyl almost periodic functions on locally compact Abelian groups, which naturally appear in the theory of aperiodic order.

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.

We study uniform and non-uniform model sets in arbitrary locally compact second countable (lcsc) groups, which provide a natural generalization of uniform model sets in locally compact abelian groups as defined by Meyer and used as…

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 model set is a model set in some modified cut-and-project scheme…

A locally-optimal structure is a combinatorial structure such as a maximal independent set that cannot be improved by certain (greedy) local moves, even though it may not be globally optimal. It is trivial to construct an independent set in…

The main purpose of this paper is to prove the mean ergodic theorem for nonexpansive mappings and semigroups in locally compact Hadamard spaces, including finite dimensional Hadamard manifolds. The main tool for proving ergodic convergence…

In this work, we provide a way of constructing new semiorthogonal decompositions using metric techniques (\`a la Neeman). Given a semiorthogonal decomposition on a category with a special kind of metric, which we call a compressible metric,…

We study the structure of invariant measures for continuous automorphisms of compact metrizable abelian groups satisfying the descending chain condition. We show that the finitely supported invariant measures are weak-* dense in the space…

Almost block diagonal linear systems of equations can be exemplified by two modules. This makes it possible to construct all sequential forms of band and/or block elimination methods, six old and fourteen new. It allows easy assessment of…

We construct Fourier transforms relating functions and distributions on finite height $p$-divisible rigid analytic groups and objects in a dual category of $\mathbb{Z}_p$-local systems with analyticity conditions. Our Fourier transforms are…

This paper introduces shape boundary regions in descriptive proximity forms of CW (Closure-finite Weak) spaces as a source of amiable fixed subsets as well as almost amiable fixed subsets of descriptive proximally continuous (dpc) maps. A…

Let $G$ be a locally compact group with the left Haar measure $m_{G}$. A probability measure ${\mu}$ on $G$ is said to be strictly aperiodic if the support of ${\mu}$ is not contained in a proper closed left coset of $G$. In this paper, we…

Given a cut and project scheme and a pre-compact Borel window we show that almost surely all positions of the window give rise to point sets with Besicovitch almost periodic Dirac combs. In particular, all those positions lead to pure point…

We construct model sets arising from cut and project schemes in Euclidean spaces whose associated Delone dynamical systems have positive toplogical entropy. The construction works both with windows that are proper and with windows that have…

We investigate convolution semigroups of probability measures with continuous densities on locally compact abelian groups, which have a discrete subgroup such that the factor group is compact. Two interesting examples of the quotient…

An almost abelian Lie group is a solvable Lie group with a codimension-one normal abelian subgroup. We characterize almost Hermitian structures on almost abelian Lie groups where the almost complex structure is harmonic with respect to the…

Two approaches to Lipschitz structures for any set are presented, studied and compared. The first approach is similar to the one proposed in Fraser, Jr. R. B., Axiom systems for Lipschitz structures, Fundamenta Mathematicae, (1970), where…