An Integral Identity Relating Diamond and Square Domains
General Mathematics
2026-01-19 v1
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.
Keywords
Cite
@article{arxiv.2601.10764,
title = {An Integral Identity Relating Diamond and Square Domains},
author = {Agustín Domínguez-Cruz},
journal= {arXiv preprint arXiv:2601.10764},
year = {2026}
}
Comments
4 pages, 1 figure