Non-symmetric convex domains have no basis of exponentials

Details Non-symmetric convex domains have no basis of exponentials Non-symmetric convex domains have no basis of exponentials

1999-04-14

arxiv.org/abs/math/9904064v2

Mathematics

Classical Analysis and ODEs

Scientific paper

A conjecture of Fuglede states that a bounded measurable set $\Omega$ in space, of measure 1, can tile space by translations if and only if the Hilbert space $L^2(\Omega)$ has an orthonormal basis consisting of exponentials. If $\Omega$ has the latter property it is called spectral. We generalize a result of Fuglede, that a triangle in the plane is not spectral, proving that every non-symmetric convex domain is not spectral.

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