2 papers
math.CA2001
Fuglede conjecture holds for convex planar domains
Alex Iosevich, Nets Katz, Terry Tao
Let be a compact convex domain in the plane. We prove that has an orthogonal basis of exponentials if and only if tiles the plane by translation.
math.CA1999
Convex bodies with a point of curvature do not have Fourier bases
Alex Iosevich, Nets Hawk Katz, Terence Tao
We prove that no smooth symmetric convex body with at least one point of non-vanishing Gaussian curvature can admit an orthogonal basis of exponentials. (The non-symmetric case…