Aperiodic Order, Part 2

Front Cover
Cambridge University Press, 2013 - Mathematics - 404 pages
Quasicrystals are non-periodic solids that were discovered in 1982 by Dan Shechtman, Nobel Laureate in Chemistry 2011. The mathematics that underlies this discovery or was stimulated by it, which is known as the theory of Aperiodic Order, is the subject of this comprehensive multi-volume series. This second volume begins to develop the theory in more depth. A collection of leading experts in the field, among them Robert V. Moody, introduce and review important aspects of this rapidly-expanding field. The volume covers various aspects of crystallography, generalising appropriately from the classical case to the setting of aperiodically ordered structures. A strong focus is placed upon almost periodicity, a central concept of crystallography that captures the coherent repetition of local motifs or patterns, and its close links to Fourier analysis, which is one of the main tools available to characterise such structures. The book opens with a foreword by Jeffrey C. Lagarias on the wider mathematical perspective and closes with an epilogue on the emergence of quasicrystals from the point of view of physical sciences, written by Peter Kramer, one of the founders of the field on the side of theoretical and mathematical physics. -- from back cover.
 

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Contents

Geometric Enumeration Problems for Lattices
73
Almost Periodic Measures and their Fourier Transforms
173
Almost Periodic Pure Point Measures
271
Averaging Almost Periodic Functions along
343
Epilogue Gateways Towards Quasicrystals
363
Index
381
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About the author (2013)

Michael Baake is a Professor of Mathematics at Universitšt Bielefeld, Germany.

Uwe Grimm is a Professor of Mathematics at The Open University, Milton Keynes.