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- W4297904210 abstract "J.C.Lagarias (2000) conjectured that if $mu$ is a complex measure on p-dimensional Euclidean space with a uniformly discrete support and its spectrum (Fourier transform) is also a measure with a uniformly discrete support, then the support of $mu$ is a subset of a finite union of shifts of some full-rank lattice. The conjecture was proved by N.Lev and A.Olevski (2013) in the case p=1. In the case of an arbitrary p they proved the conjecture only for positive measures. Here we show that Lagarias' conjecture is false in the general case and find two new special cases when assertion of the conjecture is valid." @default.
- W4297904210 created "2022-10-01" @default.
- W4297904210 creator A5082268225 @default.
- W4297904210 date "2015-02-28" @default.
- W4297904210 modified "2023-09-26" @default.
- W4297904210 title "Fourier quasicrystals and Lagarias' conjecture" @default.
- W4297904210 doi "https://doi.org/10.48550/arxiv.1503.00172" @default.
- W4297904210 hasPublicationYear "2015" @default.
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