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Book DetailsFields Institute MonographsVolume: 10; 1998; 289 ppMSC: Primary 20; 52; 11
The common topic of the eleven articles in this volume is ordered aperiodic systems realized either as point sets with the Delone property or as tilings of a Euclidean space. This emerging field of study is found at the crossroads of algebra, geometry, Fourier analysis, number theory, crystallography, and theoretical physics. The volume brings together contributions by leading specialists. Important advances in understanding the foundations of this new field are presented.
Titles in this series are co-published with The Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).
ReadershipMathematicians, physicists, crystallographers; graduate students.
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Table of Contents
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Chapters
-
Similarity submodules and semigroups
-
Pisot-cyclotomic quasilattices and their symmetry semigroups
-
Three possible branches of determinate modular generalization of crystallography
-
Non-crystallographic root systems
-
Upper bounds for the lengths of bridges based on Delone sets
-
The local theorem for tilings
-
Uniform distribution and the projection method
-
One corona is enough for the Euclidean plane
-
Cut-and-project sets in locally compact Abelian groups
-
Spectrum of dynamical systems arising from Delone sets
-
Non-locality and aperiodicity of $d$-dimensional tilings
-
-
RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
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The common topic of the eleven articles in this volume is ordered aperiodic systems realized either as point sets with the Delone property or as tilings of a Euclidean space. This emerging field of study is found at the crossroads of algebra, geometry, Fourier analysis, number theory, crystallography, and theoretical physics. The volume brings together contributions by leading specialists. Important advances in understanding the foundations of this new field are presented.
Titles in this series are co-published with The Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).
Mathematicians, physicists, crystallographers; graduate students.
-
Chapters
-
Similarity submodules and semigroups
-
Pisot-cyclotomic quasilattices and their symmetry semigroups
-
Three possible branches of determinate modular generalization of crystallography
-
Non-crystallographic root systems
-
Upper bounds for the lengths of bridges based on Delone sets
-
The local theorem for tilings
-
Uniform distribution and the projection method
-
One corona is enough for the Euclidean plane
-
Cut-and-project sets in locally compact Abelian groups
-
Spectrum of dynamical systems arising from Delone sets
-
Non-locality and aperiodicity of $d$-dimensional tilings
