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Quasicrystals and Poisson’s summation formula

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Abstract

We characterize the measures on \(\mathbb {R}\) which have both their support and spectrum uniformly discrete. A similar result is obtained in \(\mathbb {R}^n\) for positive measures.

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Authors and Affiliations

  1. Department of Mathematics, Bar-Ilan University, 52900 , Ramat Gan, Israel

    Nir Lev

  2. School of Mathematical Sciences, Tel-Aviv University, 69978 , Tel Aviv, Israel

    Alexander Olevskii

Authors
  1. Nir Lev
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  2. Alexander Olevskii
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Corresponding author

Correspondence to Nir Lev.

Additional information

N. Lev and A. Olevskii are partially supported by their respective Israel Science Foundation grants.

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Lev, N., Olevskii, A. Quasicrystals and Poisson’s summation formula. Invent. math. 200, 585–606 (2015). https://doi.org/10.1007/s00222-014-0542-z

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  • DOI: https://doi.org/10.1007/s00222-014-0542-z

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