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Unverified50% confidenceFactExact time

Benedicks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=0

1

Sources

50%

Confidence

Long-term

Relevance

8/22/2026

First Seen

Sources

研究生证明分形上的量子不确定性原理：跨越傅里叶分析与几何的突破

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≡068% similar UnverifiedHardy、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）66% similar UnverifiedFrostman引理（1935年）断言：如果紧集的s维Hausdorff测度为正，则该集合上存在非零正则Borel测度μ满足μ(B(x,r)) ≤ C·r^s64% similar Unverified2018年Rodgers和Tao证明了De Bruijn-Newman常数Λ≥064% similar Unverified黎曼猜想认为黎曼zeta函数的非平凡零点的实部都等于1/2，全部落在临界线上59% similar

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