Directions in mathematical quasicrystals
著者
書誌事項
Directions in mathematical quasicrystals
（CRM monograph series, v. 13）
American Mathematical Society, c2000
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
This volume includes twelve solicited articles which survey the current state of knowledge and some of the open questions on the mathematics of aperiodic order. A number of the articles deal with the sophisticated mathematical ideas that are being developed from physical motivations. Many prominent mathematical aspects of the subject are presented, including the geometry of aperiodic point sets and their diffractive properties, self-affine tilings, the role of $C^*$-algebras in tiling theory, and the interconnections between symmetry and aperiodic point sets. Also discussed are the question of pure point diffraction of general model sets, the arithmetic of shelling icosahedral quasicrystals, and the study of self-similar measures on model sets.From the physical perspective, articles reflect approaches to the mathematics of quasicrystal growth and the Wulff shape, recent results on the spectral nature of aperiodic Schrodinger operators with implications to transport theory, the characterization of spectra through gap-labeling, and the mathematics of planar dimer models. A selective bibliography with comments is also provided to assist the reader in getting an overview of the field. The book will serve as a comprehensive guide and an inspiration to those interested in learning more about this intriguing subject.
目次
Self-similar measures for quasicrystals by M. Baake and R. V. Moody Fourier analysis of deformed model sets by G. Bernuau and M. Duneau Mathematical quasicrystals and the problem of diffraction by J. C. Lagarias Designer quasicrystals: Cut-and-project sets with pre-assigned properties by P. A. B. Pleasants Generalized model sets and dynamical systems by M. Schlottmann On shelling icosahedral quasicrystals by A. Weiss Tilings, $C*$-algebras, and $K$-theory by J. Kellendonk and I. F. Putnam Hulls of aperiodic solids and gap labeling theorems by J. Bellissard, D. J. L. Herrmann, and M. Zarrouati Quasicrystals, parametric density, and Wulff-shape by K. Boroczky, Jr., U. Schnell, and J. M. Wills Gordon-type arguments in the spectral theory of one-dimensional quasi-crystals by D. Damanik The planar dimer model with boundary: A survey by R. Kenyon Digit tiling of euclidean space by A. Vince A guide to quasicrystal literature by M. Baake and U. Grimm Index.
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