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arXiv · 2607.24005

Fuglede's conjecture holds for three intervals

Ruxi Shi
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Abstract

We prove that every bounded measurable subset of the real line that is both spectral and a union of three intervals tiles the line by translations, thereby completing Fuglede's conjecture for this class. The proof develops a new cofactor-rigidity method based on the secular determinant of an associated self-adjoint derivative.

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Ruxi Shi. 2026-07-27. Fuglede's conjecture holds for three intervals. https://arxiv.org/abs/2607.24005

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