108 citations · 378 across the 31 of their papers we have counts for
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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…
math.CO1999★ 5 cited
A new bound on partial sum-sets and difference-sets, and applications to the Kakeya conjecture
Nets Hawk Katz, Terence Tao
Let , be finite subsets of an abelian group, and let be such that $# A, # B, # \{a+b: (a,b) \in G \} \leq N$. We consider the question of estimating th…
math.CA1999★ 12 cited
An improved bound on the Minkowski dimension of Besicovitch sets in R^3
Nets Hawk Katz, Izabella Łaba, Terence Tao
A Besicovitch set is a set which contains a unit line segment in any direction. It is known that the Minkowski and Hausdorff dimensions of such a set must be greater than or equal…