论文标题
新的标志不确定性原则
New Sign Uncertainty Principles
论文作者
论文摘要
我们证明了新的符号不确定性原则，这些原则大大推广了Bourgain，Clozel＆Kahane和Cohn＆Gonçalves的最新发展，并将我们的结果应用于各种空间和运营商。特别是，我们为傅立叶和DINI系列建立了新的符号不确定性原理，Hilbert Transform，离散的傅立叶和Hankel变换，球形谐波和Jacobi多项式等。我们提供了数值证据，强调了傅立叶和汉克尔变换的离散和连续符号不确定性原理之间的关系，这反过来又通过线性编程与球体堆积问题有关。最后，我们探讨了球体上的不确定性原理与球形设计之间的一些联系。
We prove new sign uncertainty principles which vastly generalize the recent developments of Bourgain, Clozel & Kahane and Cohn & Gonçalves, and apply our results to a variety of spaces and operators. In particular, we establish new sign uncertainty principles for Fourier and Dini series, the Hilbert transform, the discrete Fourier and Hankel transforms, spherical harmonics, and Jacobi polynomials, among others. We present numerical evidence highlighting the relationship between the discrete and continuous sign uncertainty principles for the Fourier and Hankel transforms, which in turn are connected with the sphere packing problem via linear programming. Finally, we explore some connections between the sign uncertainty principle on the sphere and spherical designs.
