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.

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

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

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

  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.

  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.

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

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

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

  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.

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