论文标题
加博尔高斯系统的上和下密度
Upper and lower densities of Gabor Gaussian Systems
论文作者
论文摘要
我们研究完整和最小的Gabor高斯系统的上部和下密度。与经典的晶格情况相反，当它们均等于$ 1 $时，我们证明下密度可能达到$ 0 $，而高密度至少可能从$ \ frac {1}π$到$ e $不等。在上层密度超过$ 1 $的情况下，我们建立了与上部和下密度相关的急剧不平等。
We study the upper and the lower densities of complete and minimal Gabor Gaussians systems. In contrast to the classical lattice case when they are both equal to $1$, we prove that the lower density may reach $0$ while the upper density may vary at least from $\frac{1}π$ to $e$. In the case when the upper density exceeds $1$, we establish a sharp inequality relating the upper and the lower densities.
