An Introduction to Wave Packet Systems in L2(ℝ) Christensen Ole1,*, Rahimi Asghar2 1Department of Mathematics, Technical University of Denmark, Building 303, 2800, Lyngby, Denmark 2Department of Mathematics, University of Maragheh, Maragheh, Iran *Author for Correspondence. E-mail: ole.ehristensen@mat.dtu.dk
Abstract This paper gives an introduction to wave packet systems. On the one hand, it presents a sufficient condition for a wave packet system to be a frame. On the other hand, it also shows that there is a large class of parameters and functions that cannot generate a Bessel sequence. A result by Hernandez, Labate and Weiss [1] yields a characterisation of the dual pairs of these systems. Top AMS Subject Classification 42C15, 42C40. Top Keywords Frames, Dual frame, Wave packet system, Wavelet system, Gabor system, Shift-invariant system. Top |