Open Access Repository
Pure point measures with sparse support and sparse Fourier-Bohr support
Downloads
Downloads per month over past year

|
PDF
140823 - Pure p...pdf | Download (447kB) | Preview |
Abstract
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 well understood in Euclidean space, based on the use of tempered distributions. Here, we extend the theory to second countable, locally compact Abelian groups, where we can employ general cut and project schemes and the structure of weighted model combs, along with the theory of almost periodic measures. In particular, for measures with Meyer set support, we characterise sparseness of the Fourier–Bohr spectrum via conditions of crystallographic type, and derive representations of the measures in terms of trigonometric polynomials. More generally, we analyse positive definite, doubly sparse measures in a natural cut and project setting, which results in a Poisson summation type formula.
Item Type: | Article |
---|---|
Authors/Creators: | Baake, M and Strungaru, N and Terauds, V |
Keywords: | aperiodicity, pure point measures, Fourier transform |
Journal or Publication Title: | Transactions of the London Mathematical Society |
Publisher: | John Wiley & Sons Ltd |
ISSN: | 2052-4986 |
DOI / ID Number: | 10.1112/tlm3.12020 |
Copyright Information: | Copyright 2020 The Authors. Licensed under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) http://creativecommons.org/licenses/by-nc-nd/4.0/ |
Item Statistics: | View statistics for this item |
Actions (login required)
![]() |
Item Control Page |