Fuglede conjecture holds for convex planar domains

Details Fuglede conjecture holds for convex planar domains Fuglede conjecture holds for convex planar domains

2001-04-07

arxiv.org/abs/math/0104087v1

Mathematics

Classical Analysis and ODEs

Scientific paper

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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