Indian Journal of Industrial and Applied Mathematics
Open Access
  • Year: 2008
  • Volume: 1
  • Issue: 1

An Introduction to Wave Packet Systems in L2(ℝ)

  • Author:
  • Ole Christensen1,, Asghar Rahimi2
  • Total Page Count: 16
  • Published Online: Jun 1, 2008
  • Page Number: 42 to 57

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.

Keywords

42C15, 42C40, Frames, Dual frame, Wave packet system, Wavelet system, Gabor system, Shift-invariant system