Uncertainty principles and signal recovery
SIAM Journal on Applied Mathematics
The uncertainty principle on groups
SIAM Journal on Applied Mathematics
An uncertainty inequality for groups of order pq
European Journal of Combinatorics
Sub-linear root detection, and new hardness results, for sparse polynomials over finite fields
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
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Let G be a finite abelian group of order n. For a complex valued function f on G let fdenote the Fourier transform of f. The classical uncertainty inequality asserts that if f ≠ 0 then |supp(f)| ċ |supp(f)| ≥ |G|. (1) Answering a question of Terence Tao, the following improvement of (1) is shown: Theorem. Let d1 d2 be two consecutive divisors of n. If d1 ≤ k = |supp(f)| ≤ d2 then |supp(f)| ≥ n/d1d2(d1 + d2 - k).