一类特殊Gabor框的存在性

On the existence problem of some Gabor frame wavelets

通过Littlewood问题与一类Gabor框存在性的问题的等价性,借助对均匀分布在单位圆上的n个单位向量和为零的充分必要性论证,解决了n大于等于3时这类Gabor框的充分必要条件,并对此结果和已有结果进行了比较研究。

By referring to the fact that the Littlewood problem is equivalent to the existence of a kind of Gabor frame,and by invoking the necessary and sufficient conditions for the sum of any n vectors distributed uniformly on the unit circle to be zero, this paper presented necessary and sufficient condition for the problem of Gabor frame with n〉= 3. The relationship between our result and existing ones was explored.