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Mathematical aspects of quasicrystals

Aperiodic order and pure point diffraction

Pages 2059-2071 | Received 06 Dec 2007, Accepted 20 Mar 2008, Published online: 11 Oct 2010
 

Abstract

The paper gives a leisurely introduction to mathematical diffraction theory with a focus on pure point diffraction. In particular, various characterizations of pure point diffraction and common models arising from cut and project schemes are discussed. It finishes with a list of open problems.

Acknowledgements

It is my pleasure to acknowledge helpful discussions with Michael Baake when I was preparing the talk at ‘Quasicrystals – The Silver Jubilee’, Tel Aviv, 2007, out of which this article arose. I take this opportunity to thank the organizers for the invitation to a highly enjoyable conference. Financial support from the German Science Foundation (DFG) is gratefully acknowledged.

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