Gabor框架的一些结果

Some Results of Gabor Frames

设g∈L2(R),a,b>0,众所周知,只有当ab<1时,Gabor系(g,a,b)才可能构成L2(R)的框架。文中指出,如果g具有紧支集,■连续且满足单位剖分恒等式,那么当b>0,a=2,3,…时,即使ab<1,Gabor系(g,a,b)也不能构成框架。

Let g∈L2(R),a,b>0.It is well known that if Gabor system (g,a,b) is a frame for L2(R),then ab<1. In this paper,it is shown that Gabor system (g,a,b) is not a frame for L2(R) if g is a compactly supported function ,■ is a continuous function,the integer translaters of ■ constitute a partition of unity,b>0,a=2,3,… and ab<1.