An Integral Identity Relating Diamond and Square Domains
Fuente:
arXiv
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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911378696044544 |
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| author | Domínguez-Cruz, Agustín |
| author_facet | Domínguez-Cruz, Agustín |
| contents | We establish an integral identity for functions on R^2 that are invariant under discrete diagonal translations. The identity shows that integration over the diamond-shaped region |x| + |y| <= L is exactly one half of the integral over the square domain [-L, L]^2, allowing diamond-domain integrals to be reduced to easier rectangular integrations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_10764 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An Integral Identity Relating Diamond and Square Domains Domínguez-Cruz, Agustín General Mathematics We establish an integral identity for functions on R^2 that are invariant under discrete diagonal translations. The identity shows that integration over the diamond-shaped region |x| + |y| <= L is exactly one half of the integral over the square domain [-L, L]^2, allowing diamond-domain integrals to be reduced to easier rectangular integrations. |
| title | An Integral Identity Relating Diamond and Square Domains |
| topic | General Mathematics |
| url | https://arxiv.org/abs/2601.10764 |