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Discrete Wavelets Associated with DUNKL Operator on Real Line

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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Year of Publication: 2016
Authors:
C. P. Pandey, Rakesh Mohan, Bhairaw Nath Tripathi
10.5120/ijca2016907754

C P Pandey, Rakesh Mohan and Bhairaw Nath Tripathi. Article: Discrete Wavelets Associated with DUNKL Operator on Real Line. International Journal of Computer Applications 134(1):17-21, January 2016. Published by Foundation of Computer Science (FCS), NY, USA. BibTeX

@article{key:article,
	author = {C. P. Pandey and Rakesh Mohan and Bhairaw Nath Tripathi},
	title = {Article: Discrete Wavelets Associated with DUNKL Operator on Real Line},
	journal = {International Journal of Computer Applications},
	year = {2016},
	volume = {134},
	number = {1},
	pages = {17-21},
	month = {January},
	note = {Published by Foundation of Computer Science (FCS), NY, USA}
}

Abstract

Using convolution theory of the dunkl transform, discrete dunkl wavelet transform is defined. A reconstruction formula for the discrete dunkl wavelet is obtained. Important properties of the discrete dunkl wavelet are presented. Frames and Riesz basis involving dunkl wavelets are studied.

References

  1. C.K. Chui, An Introduction to Wavelets, Academic Press, New York (1992)
  2. Lokenath Debnath, Wavelet Transforms and their Applications, PINSA –A 6(1998), 685-713
  3. U.Depczynski, Sturm-Liouville wavelets, Applied and Computational Harmonic Analysis, 5(1998), 216-247.
  4. R.S. Pathak and M.M. Dixit, Continuous and discrete Bessel wavelet transforms, J. Computational and Applied Mathematics, 160 (2003), 241-250.
  5. Vagif S.GULIYEV and Yagub Y.MAMMADOV, Function Spaces and Integral Operators for The Dunkl Operators on the Real Line, Khajar Journal of Mathematics 4 (2006), 17-42.
  6. C.P.Pandey, Rakesh Mohan and B.N.Tripathi, Continuous Dunkl wavelet transform, International Journal of Current Engineering and technology , Vol 4, No.1, 2014

Keywords

Dunkl transform, wavelet transform, Dunkl operator