Title: Characterizations of p-Wavelets on Positive Half Line Using the Walsh-Fourier Transform
Author(s): Abdullah Abdullah
Pages: 77-84
Cite as:
Abdullah Abdullah, Characterizations of p-Wavelets on Positive Half Line Using the Walsh-Fourier Transform, Int. J. Anal. Appl., 10 (2) (2016), 77-84.


In this paper, we study the characterization of wavelets on positive half line by means of two basic equations in the Fourier domain. We also give another characterization of wavelets.

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  1. Abdullah, Affine and quasi-affine frames on positive half line, J. Math. Ext., in press. Google Scholar

  2. M. Bownik, On characterizations of multiwavelets in L2(Rn), Proc. Amer. Math. Soc., 129 (2001), 3265-3274. Google Scholar

  3. A. Calogero, A characterization of wavelets on general lattices, J. Geom. Anal. 10 (2000), 597-622. Google Scholar

  4. C. K. Chui, X. Shi and J. Stöckler, Affine frames, quasi-affine frames, and their duals, Adv. Comput. Math., 8 (1998), 1-17. Google Scholar

  5. Y. A. Farkov, Orthogonal p-wavelets on R+, in Proceedings of International Conference Wavelets and Splines, St. Petersberg State University, St. Petersberg (2005), 4-6. Google Scholar

  6. Y. A. Farkov, A. Y. Maksimov and S. A. Stroganov, On biorthogonal wavelets related to the Walsh functions, Int. J. Wavelets, Multiresolut. Inf. Process. 9(3) (2011), 485-499. Google Scholar

  7. G. Gripenberg, A necessary and sufficient condition for the existence of a father wavelet, Stud. Math. 114 (1995), 207-226. Google Scholar

  8. E. Hernández and G. Weiss, A First Course on Wavelets, CRC Press, New York, 1996. Google Scholar

  9. A. Ron and Z. Shen, Frames and stable bases for shift invariant subspaces of L2(Rd), Canad. J. Math., 47 (1995), 1051-1094. Google Scholar

  10. F A Shah and L. Debnath, Dyadic wavelet frames on a half-line using the Walsh-Fourier transform, Integ. Trans. Special Funct., 22(2011), 477-486. Google Scholar

  11. F. A. Shah, Tight wavelet frames generated by the Walsh polynomials, Int. J. Wavelets, Multiresolut. Inf. Process., 11 (2013), Article ID 1350042. Google Scholar


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