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arXiv · 2601.10764

An Integral Identity Relating Diamond and Square Domains

Agustín Domínguez-Cruz
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Abstract

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.

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Agustín Domínguez-Cruz. 2026-01-14. An Integral Identity Relating Diamond and Square Domains. https://arxiv.org/abs/2601.10764

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