Titelaufnahme
Titelaufnahme
- TitelPure point measures with sparse support and sparse Fourier–Bohr support
- Verfasser
- Enthalten inTransactions of the London Mathematical Society, Jg. 7 H. 1, S. 1-32
- Erschienen
- SpracheEnglisch
- DokumenttypAufsatz in einer Zeitschrift
- URN
- DOI
Zugriffsbeschränkung
- Das Dokument ist frei verfügbar
Links
- Social MediaShare
- NachweisKein Nachweis verfügbar
- IIIF
Dateien
Klassifikation
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.
Inhalt
Statistik
- Das PDF-Dokument wurde 4 mal heruntergeladen.
