论文标题
关于符号不确定性原理的规律性和质量集中现象
On regularity and mass concentration phenomena for the sign uncertainty principle
论文作者
论文摘要
波尔加因，clozel＆kahane的标志不确定性原理断言，如果功能$ f：\ mathbb {r}^d \ to \ mathbb {r} $及其傅立叶变换$ \ wideHat {f} $在起源上并不是相同的零，那么它们在派发上都不是一个非官方的社区。在本文中，我们建立了标志不确定性原理的一些等效表述，尤其是证明当$ d = 1 $时，Schwartz类中存在最小化序列。我们进一步解决了互补的不确定性原理，并表明相应的近距离二聚体将其在所有维度上起源附近的正质量的普遍比例集中在所有维度上。
The sign uncertainty principle of Bourgain, Clozel & Kahane asserts that if a function $f:\mathbb{R}^d\to \mathbb{R}$ and its Fourier transform $\widehat{f}$ are nonpositive at the origin and not identically zero, then they cannot both be nonnegative outside an arbitrarily small neighborhood of the origin. In this article, we establish some equivalent formulations of the sign uncertainty principle, and in particular prove that minimizing sequences exist within the Schwartz class when $d=1$. We further address a complementary sign uncertainty principle, and show that corresponding near-minimizers concentrate a universal proportion of their positive mass near the origin in all dimensions.
