Indian Journal of Industrial and Applied Mathematics
  • Year: 2012
  • Volume: 3
  • Issue: 1

Wavelet Frames on Direct Products of Cyclic Groups

  • Author:
  • Firdous Ahmad Shah1,, Abul Hasan Siddiqi2,
  • Total Page Count: 12
  • Published Online: Dec 1, 2012
  • Page Number: 32 to 43

1Department of Mathematics, University of Kashmir South Campus, Anantnag-192101, Jammu and Kashmir, India

2Department of Mathematics, Sharada University Knowledge Park-III, Greater Noida-201306, India

*Author for Correspondence. E-mail: fashah79@gmail.com

** E-mail: siddiqi. abulhasan@gmail.com

Abstract

In this paper, we study the construction of wavelet frames on a locally compact Abelian group G which is the weak direct product of a countable set of cyclic groups of pth order. We establish necessary and sufficient conditions for the system {ψj, k}(j, h) ∈ ℤ × H to be a wavelet frame in L2(G).

Keywords

Wavelet, wavelet frame, locally compact Abelian group, cyclic group, Walsh function, Walsh-Fourier transform, 42A38, 42A55, 42C40, 42C10