本文主要研究L^2(R^d)上的Gabor系成为框架或框架序列的特征。首先在时域上给出了Gabor系成为L^2(R^d)上框架或框架序列的两个充分条件,并得到在特殊情形了Gabor系成为框架序列的充要条件。最后在频域上也给出了相应的结果。
The purpose of this paper is to characterize a Gabor system which generates a frame or a frame sequence for L^2(R^d). Proved are two sufficient conditions with which the Gabor system can be a frame or a frame sequence for L^2(R^d) in time domain. Under some special cases, the sufficient conditions are also necessary. The analogous results in frequency domain are also given at the end of the paper.