Mathematical Research Letters

Volume 10 (2003)

Number 5

The Fuglede spectral conjecture holds for convex planar domains

Pages: 559 – 569



Alex Iosevich (University of Missouri, Columbia)

Nets Katz (Washington University in St. Louis)

Terence Tao (University of California at Los Angeles)


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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