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.
Mathematics Subject Classification (2010). Primary 42A38, 37A50; Secondary 37B10, 52C23.
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© 2015 Springer Basel
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Baake, M., Birkner, M., Grimm, U. (2015). Non-Periodic Systems with Continuous Diffraction Measures. In: Kellendonk, J., Lenz, D., Savinien, J. (eds) Mathematics of Aperiodic Order. Progress in Mathematics, vol 309. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0903-0_1
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DOI: https://doi.org/10.1007/978-3-0348-0903-0_1
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-0902-3
Online ISBN: 978-3-0348-0903-0
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