PreprintCC BY 4.0arXiv
Spectral unions of four intervals tile the real line
Abstract
We prove that every spectral union of four bounded intervals tiles the real line by translations. The argument combines periodicity of spectra, cofactor identities for the secular determinant, and a common tiling complement for the finite spectral fibers. We also establish a rigidity theorem for six complex numbers with prescribed vanishing power sums.
Related
- Spectral unions of intervals with few rational relation tile the real line
- Countable unions of intervals without Riesz spectra
- Perturbed Exponential Systems, Pattern-Dependent Shifted-Sinc Operators, and Matrix Symbols on Finite Unions of Intervals
- Stein neighborhood bases for complex--totally real unions
- Luo's Spectral Large Sieve Inequality on Short Intervals
BibTeX
@misc{bell2026spectral,
title = {{Spectral unions of four intervals tile the real line}},
author = {Alexander Okezue Bell},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37975},
eprint = {2610.37975},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37975},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Spectral unions of four intervals tile the real line
AU - Alexander Okezue Bell
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37975
UR - https://arxiv.org/abs/2610.37975
AB - We prove that every spectral union of four bounded intervals tiles the real line by translations. The argument combines periodicity of spectra, cofactor identities for the secular determinant, and a common tiling complement for the finite spectral fibers. We also establish a rigidity theorem for six complex numbers with prescribed vanishing power sums.
ER -