Abstract
We find new simple conditions for a support of a discrete measure on Euclidean space to be a finite union of translated lattices. The arguments are based on a local analog of Wiener’s Theorem on absolutely convergent trigonometric series and theory of almost periodic functions.
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Communicated by Karlheinz Gröchenig.
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Favorov, S.Y. Large Fourier Quasicrystals and Wiener’s Theorem. J Fourier Anal Appl 25, 377–392 (2019). https://doi.org/10.1007/s00041-017-9576-0
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DOI: https://doi.org/10.1007/s00041-017-9576-0
Keywords
- Distribution
- Fourier transform
- Measure with discrete support
- Spectrum of measure
- Almost periodic measure
- Lattice
- Weiner’s Theorem