Indian Journal of Industrial and Applied Mathematics
  • Year: 2015
  • Volume: 6
  • Issue: 2

NonuniformWave Packet Frames in L2 (ℝ)

1Research Scholar, Department of Mathematics, Guru Nanak Dev University, Amritsar, 143005, Punjab, India

2Professor, Department of Mathematics, Guru Nanak Dev University, Amritsar, 143005, Punjab, India

*(Corresponding Author) E-mail id: vikramsharma6898@gmail.com

**pmanch2k1@yahoo.co.in

Abstract

In this paper, we construct wave packet frames in L2(ℝ) over a translation set Λ, which is not necessarily a group. We call it nonuniform wave packet frame. We present a necessary and sufficient condition for the wave packet system {D(2N)jTλEcmψ}j,m∈ℤ,λ∈Λ. to be a frame for L2(ℝ).

Keywords

Wavelet, Frame, Wave packet frame, Fourier transform, 42A38, 42A55, 42C10, 42C15, 42C40