Exact and approximate expansions with pure Gaussian wave packets (Q2878997)

Wave packets as generalisations of wavelet approximations are a most successful tool in the approximation especially of Fourier integral operators. In this paper, wave packets from function spaces spanned by Gaussian functions (exponentials) are constructed and analysed just for this purpose. Among other subjects, frame operators using the said wave packets are studied, asymptotical estimates are made, expansions are considered and decay estimates are provided. The use especially of parabolic dilation and rotation on top of translation makes this article particularly interesting.