Analogues of Fourier quasicrystals for a strip
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912144724852736 |
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| author | Favorov, Sergii |
| author_facet | Favorov, Sergii |
| contents | We study a certain family of discrete measures with unit masses on a horizontal strip as an analogue of Fourier quasicrystals on the real line. We prove a one-to-one correspondence between supports of measures from this family and zero sets of exponential polynomials with imaginary frequencies. This result is the special case of a general result on measures whose supports correspond to zero sets of absolutely convergent Dirichlet series with bounded spectrum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_09563 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Analogues of Fourier quasicrystals for a strip Favorov, Sergii Functional Analysis Complex Variables 52C23, 30B50, 32A60, We study a certain family of discrete measures with unit masses on a horizontal strip as an analogue of Fourier quasicrystals on the real line. We prove a one-to-one correspondence between supports of measures from this family and zero sets of exponential polynomials with imaginary frequencies. This result is the special case of a general result on measures whose supports correspond to zero sets of absolutely convergent Dirichlet series with bounded spectrum. |
| title | Analogues of Fourier quasicrystals for a strip |
| topic | Functional Analysis Complex Variables 52C23, 30B50, 32A60, |
| url | https://arxiv.org/abs/2408.09563 |