L^2(R^d)上Gabor框架的一个充分条件

A Sufficient Condition of Gabor Frames for L^2(R^d)

研究了L2(Rd)上的以矩阵平移和调制的Gabor框架的一个充分条件.首先在时域上给出了以矩阵平移和调制的Gabor框架恒等式的证明,然后给出了Gabor框架的一个充分条件的证明.最后在频域上也给出了相应的结论.

This paper is an expository survey of results on a sufficient condition of Gabor frame with matrical translation and modulation for L^2 （R^d） . First, the paper offers the proof of the identity of Gabor frames with matrical translation and modulation for L^2 （R^d） in time domain, and then it gives a sufficient condition of Gabor frame with matrical translation and modulation for L^2 （R^d） . The relevant results in frequency domain are given in the end.