Fuglede’s conjecture is false in 5 and higher dimensions

Abstract

We give an example of a set Ω ⊂ R 5 which is a finite union of unit cubes, such that L 2 (Ω) admits an orthonormal basis of exponentials { 1 |Ω|1/2 e 2πiξj ·x :

Locations

• Mathematical Research Letters - View - PDF
• arXiv (Cornell University) - PDF
• arXiv (Cornell University) - PDF
• arXiv (Cornell University) - View
• Mathematical Research Letters - View - PDF
• arXiv (Cornell University) - PDF
• arXiv (Cornell University) - PDF
• arXiv (Cornell University) - View