Mathematical Research Letters

Volume 10, Issue 5, September 2003 pp. 559-569.

The Fuglede spectral conjecture holds for convex planar domains

Authors: Alex Iosevich, Nets Katz, and Terence Tao
Author institution: University of Missouri Columbia, Washington University in St.Louis, and UCLA

Summary: Let $\Omega$ be a compact convex domain in the plane. We prove that $L^2(\Omega)$ has an orthogonal basis of exponentials if and only if $\Omega$ tiles the plane by translation.

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