Some properties of Fourier quasicrystals and measures on a strip
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911671810785280 |
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| author | Favorov, Sergii Deǧer, Özkan |
| author_facet | Favorov, Sergii Deǧer, Özkan |
| contents | In our paper we extend some results of the theory of Fourier quasicrystals on the real line to a horizontal strip of finite width. For measures in a strip we use a natural generalization of the usual Fourier transform
for measures on the line. We consider positive or translation bounded measures $μ$ on a strip whose Fourier transform is a pure point measure $\hatμ=\sum_{γ\inΓ}b_γδ_γ$ (as usual, $δ_γ$ is the unit mass at the point $γ$). We prove that the measure $ν=\sum_{γ\inΓ}|b_γ|^2δ_γ$ has the exponential growth. Moreover, if for some $η>0$ the points of $Γ$ in every interval of length $η$ are linearly independent over integers, then the measure $\hatμ$ also has the exponential growth. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_10766 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Some properties of Fourier quasicrystals and measures on a strip Favorov, Sergii Deǧer, Özkan Functional Analysis Metric Geometry 52C23, 42A38, 42A75 In our paper we extend some results of the theory of Fourier quasicrystals on the real line to a horizontal strip of finite width. For measures in a strip we use a natural generalization of the usual Fourier transform for measures on the line. We consider positive or translation bounded measures $μ$ on a strip whose Fourier transform is a pure point measure $\hatμ=\sum_{γ\inΓ}b_γδ_γ$ (as usual, $δ_γ$ is the unit mass at the point $γ$). We prove that the measure $ν=\sum_{γ\inΓ}|b_γ|^2δ_γ$ has the exponential growth. Moreover, if for some $η>0$ the points of $Γ$ in every interval of length $η$ are linearly independent over integers, then the measure $\hatμ$ also has the exponential growth. |
| title | Some properties of Fourier quasicrystals and measures on a strip |
| topic | Functional Analysis Metric Geometry 52C23, 42A38, 42A75 |
| url | https://arxiv.org/abs/2605.10766 |