Bounded common fundamental domains for two lattices
Abstract
We prove that for any two lattices L , M ⊆ R d of the same volume there exists a measurable, bounded, common fundamental domain of them. In other words, there exists a bounded measurable set E ⊆ R d such that E tiles R d when translated by L or by M . A consequence of this is that the indicator function of E forms a Weyl–Heisenberg (Gabor) orthogonal basis of L 2 ( R d ) when translated by L and modulated by ⁎ M ⁎ , the dual lattice of M .
Fields of Study & Subjects
Rings
Modules
and Algebras
Analytic and geometric function theory
Holomorphic and Operator Theory
Publication details
- Journal / source
- Advances in Mathematics
- Publisher
- Elsevier BV
- Volume
- 487
- Pages
- 110776–110776
- Publication date
- 8 January 2026
- Language
- EN