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The Inverse Problem of Pure Point Diffraction—Examples and Open Questions

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Abstract

This paper considers some open questions related to the inverse problem of pure point diffraction, in particular, what types of objects may diffract, and which of these may exhibit the same diffraction. Some diverse objects with the same simple lattice diffraction are constructed, including a tempered distribution that is not a measure, and it is shown that there are uncountably many such objects in the diffraction solution class of any pure point diffraction measure with an infinite supporting set.

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Authors and Affiliations

  1. School of Mathematics and Physics, University of Tasmania, GPO Box 252C-37, Hobart, Tasmania, 7001, Australia

    Venta Terauds

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  1. Venta Terauds
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Correspondence to Venta Terauds.

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Much of this research was undertaken at the University of Bielefeld with the support of the RCM2 and the German Research Council (DFG), via the CRC 701. The author would like to thank Michael Baake for facilitating her stay at the University of Bielefeld and for many helpful discussions relating to this work.

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Terauds, V. The Inverse Problem of Pure Point Diffraction—Examples and Open Questions. J Stat Phys 152, 954–968 (2013). https://doi.org/10.1007/s10955-013-0790-0

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  • DOI: https://doi.org/10.1007/s10955-013-0790-0

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