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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.

URL: http://www.springer.com/en/book/9783034809023
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Abstract

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.

Item Type: Book Section
Copyright Holders: 2015 Springer, Basel
ISBN: 3-0348-0902-6, 978-3-0348-0902-3
Keywords: kinematic diffraction; random dynamical systems; stationary stochastic processes
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 44126
Depositing User: Uwe Grimm
Date Deposited: 20 Aug 2015 13:16
Last Modified: 07 Dec 2018 10:34
URI: http://oro.open.ac.uk/id/eprint/44126
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