Non-negative crystalline and Poisson measures in the Euclidean space
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909179950661632 |
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| author | Favorov, Serhii |
| author_facet | Favorov, Serhii |
| contents | We study properties of temperate non-negative purely atomic measures in the Euclidean space such that the distributional Fourier transform of these measures are pure point ones. A connection between these measures and almost periodicity is shown, several forms of the uniqueness theorem are proved. We also obtain necessary and sufficient conditions for a measure with positive integer masses on the real line to correspond the zero set of an absolutely convergent Dirichlet series with bounded spectrum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_15448 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-negative crystalline and Poisson measures in the Euclidean space Favorov, Serhii Functional Analysis primary 30B50, secondary 42A38, 52S23 We study properties of temperate non-negative purely atomic measures in the Euclidean space such that the distributional Fourier transform of these measures are pure point ones. A connection between these measures and almost periodicity is shown, several forms of the uniqueness theorem are proved. We also obtain necessary and sufficient conditions for a measure with positive integer masses on the real line to correspond the zero set of an absolutely convergent Dirichlet series with bounded spectrum. |
| title | Non-negative crystalline and Poisson measures in the Euclidean space |
| topic | Functional Analysis primary 30B50, secondary 42A38, 52S23 |
| url | https://arxiv.org/abs/2404.15448 |