CHARACTERIZATIONS OF THE MULTIVARIATE WAVE PACKET SYSTEMS

Abstract

Some characterizations of the multivariate wave packet systems in terms of the Fourier transforms of the wave packet systems' generating functions are discussed in this paper. First, the characterizations of the orthogonal wave packet systems are provided. Secondly, a sufficient condition of the completeness of wave packet system in some special cases is established. Finally, the necessary conditions and sufficient conditions for the wave packet systems to be wave packet Parseval frames with the very general lattices are obtained. Thus, the corresponding known results in Gabor systems and wavelet systems are obtained as some corollaries.