论文标题
$ s^2 $的统一边界的球形谐波和量子谐波
Uniformly bounded spherical harmonics and quantum ergodicity on $S^2$
论文作者
论文摘要
在二维单位球体上，我们在球体上的点分布条件下构建了任意程度的统一边界的球形谐波。它扩展了Bourgain，Shiffman和Marzo-Ortega-Cerda的奇数领域的结果。此外，我们表明，本文构建的球形谐波在相空间中均等分布，即它们是量子的。它提供了laplacian本征函数的第一个例子，这些例子均均匀地界限和量子。
On the two-dimensional unit sphere, we construct uniformly bounded spherical harmonics of arbitrary degree, under a condition of point distribution on the sphere. It extends the results on odd-dimensional spheres by Bourgain, Shiffman, and Marzo-Ortega-Cerda. Moreover, we show that the spherical harmonics constructed in this paper are equidistributed in the phase space, i.e., they are quantum ergodic. It provides the first example of Laplacian eigenfunctions which are both uniformly bounded and quantum ergodic.
