Related papers: Almost periodic discrete sets

For metrizable spaces we replace the notion of almost periodic homeomorphism with a similar notion and verify that the usual characterizations of almost periodic homeomorphisms of compact metric spaces are valid for all metrizable spaces.

This note is a contribution to large scale geometry. More precisely, we introduce the intrinsically quasi-isometric sections in metric spaces and we investigate their properties: the Ahlfors-David regularity in large scale; following…

In this paper, we analyze multi-dimensional Besicovitch almost periodic type functions. We clarify the main structural properties for the introduced classes of Besicovitch almost periodic type functions, explore the notion of…

In this paper, we will discuss the notion of almost orthogonality in a functional sequence.Especially, we will define a few sequences of almost orthogonal polynomials which can be used successfully for modeling of electronic systems which…

The paper studies different variants of almost periodicity notion. We introduce the class of eventually strongly almost periodic sequences where some suffix is strongly almost periodic (=uniformly recurrent). The class of almost periodic…

The aim of this paper is to discus the relations between various notions of sequential completeness and the corresponding notions of completeness by nets or by filters in the setting of quasi-metric spaces. We propose a new definition of…

We introduce the class of almost symmetric submanifolds of Euclidean space, a close relative of symmetric submanifolds and (contact) sub-Riemannian symmetric spaces. More specifically, we prove that every full irreducible almost symmetric…

We show that a homeomorphism of Euclidean space is quasiconformal if and only if at each point there exists a sequence of uncentered open sets with bounded eccentricity shrinking to that point whose images also have bounded eccentricity.…

A set in $\mathbb R^d$ is called almost-equidistant if for any three distinct points in the set, some two are at unit distance apart. First, we give a short proof of the result of Bezdek and L\'angi claiming that an almost-equidistant set…

The almost periodic functions form a natural example of a non-separable normed space. As such, it has been a challenge for constructive mathematicians to find a natural treatment of them. Here we present a simple proof of Bohr's fundamental…

In this work we reproduce the characterization of $\Gg^s$-sets from the euclidean setting [J. London Math. Soc. 49:267-280,1994] to more general metric spaces. These sets have Hausdorff dimension at least $s$ and are closed by countable…

This paper studies regularity of perimiter quasiminimizing sets in metric measure spaces with a doubling measure and a Poincare inequality. The main result shows that the measure theoretic boundary of a quasiminimizing set coincides with…

A set of points in d-dimensional Euclidean space is almost equidistant if among any three points of the set, some two are at distance 1. We show that an almost-equidistant set in $\mathbb{R}^d$ has cardinality $O(d^{4/3})$.

Let $(X,d)$ be a finite metric space with $|X|=n$. For a positive integer $k$ we define $A_k(X)$ to be the quotient set of all $k$-subsets of $X$ by isometry, and we denote $|A_k(X)|$ by $a_k$. The sequence $(a_1,a_2,\ldots,a_{n})$ is…

In this paper, we analyze multi-dimensional $({\mathrm R}_{X},{\mathcal B})$-almost periodic type functions and multi-dimensional Bohr ${\mathcal B}$-almost periodic type functions. The main structural characterizations and composition…

We present a method that allows to distinguish between nearly periodic and strictly periodic time series. To this purpose, we employ a conservative criterion for periodicity, namely that the time series can be interpolated by a periodic…

Various versions of the classical definitions of (one- and twosided) almost periodicity for functions on groups with values in a uniform space are formulated and their equivalence is shown.

We prove that, for semi-invertible linear cocycles, Oseledets subspaces associated to ergodic measures may be approximated by Oseledets subspaces associated to periodic points.

We study discrete Schroedinger operators with analytic potentials. In particular, we are interested in the connection between the absolutely continuous spectrum in the almost periodic case and the spectra in the periodic case. We prove a…

For a family of second-order elliptic systems in divergence form with rapidly oscillating almost-periodic coefficients, we obtain estimates for approximate correctors in terms of a function that quantifies the almost periodicity of the…