Abstract
We prove that no smooth symmetric convex body Ω with at least one point of non-vanishing Gaussian curvature can admit an orthogonal basis of exponentials. (The nonsymmetric case was proven in a preprint by M. Kolountzakis). This is further evidence of Fuglede's conjecture, which states that such a basis is possible if and only if Ω can tile [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /] d by translations.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
