Necessary and sufficient conditions of the wave packet frames in L2(Rn)

The main goal of this paper is to consider the necessary and sufficient conditions of wave packet systems to be frames in higher dimensions. We establish the necessary and sufficient conditions for all kinds of wave packet frames of the different operator order in L2(Rn) with an arbitrary expanding matrix dilations, which include the corresponding results of wavelet analysis and Gabor theory as the special cases. Our way combines with some techniques in wavelet analysis and time-frequency analysis