Non-periodic Systems with Continuous Diffraction Measures

Baake, Michael; Birkner, Matthias and Grimm, Uwe (2015). Non-periodic Systems with Continuous Diffraction Measures. In: Kellendonk, Johannes; Lenz, Daniel and Savinien, Jean eds. Mathematics of Aperiodic Order. Progress in Mathematics (309). Basel: Birkhauser, pp. 1–32.



The present state of mathematical diffraction theory for systems with continuous spectral components is reviewed and extended. We begin with a discussion of various characteristic examples with singular or absolutely continuous diffraction, and then continue with a more general exposition of a systematic approach via stationary stochastic point processes. Here, the intensity measure of the Palm measure takes the role of the autocorrelation measure in the traditional approach. We furthermore introduce a 'Palm-type' measure for general complex-valued random measures that are stationary and ergodic, and relate its intensity measure to the autocorrelation measure.

Viewing alternatives


Public Attention

Altmetrics from Altmetric

Number of Citations

Citations from Dimensions
No digital document available to download for this item

Item Actions