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Quasicrystals, Diophantine approximation and algebraic numbers

  • Conference paper
Beyond Quasicrystals

Part of the book series: Centre de Physique des Houches ((LHWINTER,volume 3))

Abstract

Quasicrystals can be characterized by a remarkable Diophantine approximation property. This permits to define the dual quasicrystal Λ* as the collection of y in ℝn such that |e iy·x−1| ≤ 1 for each x in the given quasicrystal Λ. In many cases one obtains Λ** = Λ and this duality is nicely related to the spectral properties of quasicrystals.

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References

  1. Y. Meyer, Nombres de Pisot, nombres de Salem et analyse harmonique. Lecture Notes in Math., 117 (1970)Springer-Verlag.

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  2. Y. Meyer, Albegraic numbers and harmonic analysis. (1972), North-Holland.

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  3. J. Patera, The pentacrystals. These proceedings.

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  4. R. Salem, Algebraic numbers and Fouriér analysis. Boston, Heath, (1963).

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  5. R.V. Moody, Meyer sets and the finite generation of quasicrystals. (Preprint).

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  6. J.P. Gazeau, Quasicrystals and their symmetries. (Lectures given at the IIIrd International School on Symmetry and Structural Properties of Condensed Matter, POZNAN 1994, preprint).

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  7. J.P. Gazeau, Lectures on Quasicrystals and their symmetries. Charles University, Prague, June 1994.

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  8. A. Katz, A short introduction to quasicrystallography. From Number theory to physics, (M. Waldschmidt al. ed.) Springer-Verlag, Berlin (1992).

    Google Scholar 

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Author information

Authors and Affiliations

  1. CEREMADE, Université Paris-Dauphine, Place de Lattre de Tassigny, 75775, Paris Cedex 16, France

    Yves Meyer

Authors
  1. Yves Meyer
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Editor information

Editors and Affiliations

  1. Université Paris VII-Denis Diderot, France

    Françoise Axel

  2. CECN-CNRS, Vitry, France

    Denis Gratias

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© 1995 Springer-Verlag Berlin Heidelberg

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Meyer, Y. (1995). Quasicrystals, Diophantine approximation and algebraic numbers. In: Axel, F., Gratias, D. (eds) Beyond Quasicrystals. Centre de Physique des Houches, vol 3. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03130-8_1

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  • DOI: https://doi.org/10.1007/978-3-662-03130-8_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-59251-8

  • Online ISBN: 978-3-662-03130-8

  • eBook Packages: Springer Book Archive

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