Aperiodic Order, Part 2
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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Abelian group algebraic Aperiodic Order autocorrelation Baake Banach space Bragg peaks coincidence isometries coincidence rotations compact set compare AO1 continuous convergence convex Corollary Cu(G cubic lattices defined Delone set denote Dirac comb discrete tomography equivalent exists finite measure following result Fourier transformable function f generalisation given hence Hurwitz quaternions inflation rule integer isometries Lemma linear locally finite Math MCSLs metrisable Meyer set model set multiplicative norm norm-almost periodic ordinary CSLs periodic functions periodic measures positive definite prime primitive problem properties Proposition prototiles prove quasicrystals quaternions Radon measure relatively dense SAP(G Scalf scalM Section SSLs strongly almost periodic sublattices subset subspace sup-almost periodic symmetry Theorem theory tiling uniformly discrete vectors WAP(G weak topology weakly almost periodic weakly compact X-rays Z-module Λε