Unverified50% confidenceFactExact time
Hardy、Benedicks、Amrein-Berthier等人证明了函数及其傅里叶变换的支撑集不能同时具有有限测度（除非函数为零）
1
Sources
50%
Confidence
Long-term
Relevance
8/21/2026
First Seen
Sources
Related Claims
UnverifiedHardy在1933年证明：如果函数f(x)和其傅里叶变换都以高斯函数e^{-πx²}速率衰减，则f必须是高斯函数的常数倍；衰减更快则f≡070% similarUnverifiedThe Riemann Hypothesis states that the real parts of all non-trivial zeros of the Riemann zeta function are equal to 1/2, all lying on the critical line.69% similarUnverifiedIn 2019, Griffin, Ono, Rolen, and Zagier published work linking the Riemann Hypothesis to the hyperbolicity of Jensen polynomials, proving that Jensen polynomials associated with the Riemann ξ function are hyperbolic for sufficiently large degrees.66% similarUnverifiedBenedicks在1985年证明：如果f和其傅里叶变换的支撑集都具有有限Lebesgue测度，则f=066% similarUnverified海森堡不确定性原理在数学上本质是关于一个函数及其傅里叶变换不能同时高度集中的定理64% similar
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