Higher Dimensional Fourier Quasicrystals from Lee-Yang Varieties
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866910004632616960 |
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| author | Alon, Lior Kummer, Mario Kurasov, Pavel Vinzant, Cynthia |
| author_facet | Alon, Lior Kummer, Mario Kurasov, Pavel Vinzant, Cynthia |
| contents | In this paper, we construct Fourier quasicrystals with unit masses in arbitrary dimensions. This generalizes a one-dimensional construction of Kurasov and Sarnak. To do this, we employ a class of complex algebraic varieties avoiding certain regions in $\mathbb{C}^n$, which generalize hypersurfaces defined by Lee-Yang polynomials. We show that these are Delone almost periodic sets that have at most finite intersection with every discrete periodic set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_11184 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Higher Dimensional Fourier Quasicrystals from Lee-Yang Varieties Alon, Lior Kummer, Mario Kurasov, Pavel Vinzant, Cynthia Mathematical Physics Algebraic Geometry Complex Variables Functional Analysis 52C23, 42B10, 42A75, 42A38, 14P05 In this paper, we construct Fourier quasicrystals with unit masses in arbitrary dimensions. This generalizes a one-dimensional construction of Kurasov and Sarnak. To do this, we employ a class of complex algebraic varieties avoiding certain regions in $\mathbb{C}^n$, which generalize hypersurfaces defined by Lee-Yang polynomials. We show that these are Delone almost periodic sets that have at most finite intersection with every discrete periodic set. |
| title | Higher Dimensional Fourier Quasicrystals from Lee-Yang Varieties |
| topic | Mathematical Physics Algebraic Geometry Complex Variables Functional Analysis 52C23, 42B10, 42A75, 42A38, 14P05 |
| url | https://arxiv.org/abs/2407.11184 |