Uncertainty Principles and Light Cones
Uncertainty Principles and Light Cones
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不确定性原理和光锥
DOI：
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发表时间：
2015
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通讯作者：
B. Demange
中科院分区：
文献类型：
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作者：
B. Demange
我们证明了 Hardy 类型的不确定性原理，对于任意签名的非简并二次形式 $$q$$q，该原理限制了在锥体 $$q=0$$q=0 附近定位分布及其傅里叶变换的可能性。我们给出的结果是众所周知的正定$$q$$q。我们描述了在这种情况下优化不确定性原理的两种分布。第一种类型是分布 $$f$$f，使得 $$f$$f 和 $$widehat{f}$$f^ 在锥体 $$q=0$$q=0 上得到支持。第二种类型是仅依赖于 $$q$$q 的分布，本质上是它们自己的傅立叶变换，并且像高斯函数一样衰减，如 $$|q|
ightarrow infty $$|q|→∞。
We prove uncertainty principles of Hardy type that limit the possibility to localize a distribution and its Fourier transform near the cone $$q=0$$q=0, for a non-degenerate quadratic form $$q$$q of arbitrary signature. The results we present are well known for positive definite $$q$$q. We describe two types of distributions that optimize the uncertainty principle in this case. The first type are the distributions $$f$$f such that $$f$$f and $$widehat{f}$$f^ are supported on the cone $$q=0$$q=0. The second type are distributions that depend only on $$q$$q, that are essentially their own Fourier transform, and that decay like Gaussian functions as $$|q|
ightarrow infty $$|q|→∞.