Pure point diffraction and cut and project schemes for measures: the smooth case |
| |
Authors: | Daniel Lenz Christoph Richard |
| |
Institution: | 1.Fakult?t für Mathematik,TU Chemnitz,Chemnitz,Germany;2.Fakult?t für Mathematik,Universit?t Bielefeld,Bielefeld,Germany |
| |
Abstract: | We present a cut and project formalism based on measures and continuous weight functions of sufficiently fast decay. The emerging
measures are strongly almost periodic. The corresponding dynamical systems are compact groups and homomorphic images of the
underlying torus. In particular, they are strictly ergodic with pure point spectrum and continuous eigenfunctions. Their diffraction
can be calculated explicitly. Our results cover and extend corresponding earlier results on dense Dirac combs and continuous
weight functions with compact support. They also mark a clear difference in terms of factor maps between the case of continuous
and non-continuous weight functions.
Dedicated to Robert V. Moody on the occasion of his 65th birthday |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|