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Asymptotic Expansion of Wavelet Transform

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DOI: 10.4236/apm.2015.51002    3,215 Downloads   3,638 Views   Citations

ABSTRACT

In the present paper, we obtain asymptotic expansion of the wavelet transform for large value of dilation parameter a by using López technique. Asymptotic expansion of Shannon wavelet, Morlet wavelet and Mexican Hat wavelet transform are obtained as special cases.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Pathak, A. , Yadav, P. and Dixit, M. (2015) Asymptotic Expansion of Wavelet Transform. Advances in Pure Mathematics, 5, 21-26. doi: 10.4236/apm.2015.51002.

References

[1] Pathak, R.S. (2009) The Wavelet Transform. Atlantis Press/World Scientific, Amsterdam.
[2] López, J.L. (2007) Asymptotic Expansions of Mellin Convolutions by Means of Analytic Continuation. Journal of Computational and Applied Mathematics, 200, 628-636.
http://dx.doi.org/10.1016/j.cam.2006.01.019
[3] Pathak, R.S. and Pathak, A. (2009) Asymptotic Expansion of Wavelet Transform for Small Value a. In: Pathak, R.S. and Chui, C.K., Eds., The Wavelet Transform, World Scientific, Amsterdam, 164-169.
[4] Pathak, R.S. and Pathak, A. (2009) Asymptotic Expansion of Wavelet Transform with Error Term. In: Pathak, R.S. and Chui, C.K., Eds., The Wavelet Transform, World Scientific, Amsterdam, 154-164.
[5] Pathak, R.S. and Pathak, A. (2009) Asymptotic Expansions of the Wavelet Transform for Large and Small Values of b. The International Journal of Mathematics and Mathematical Sciences, 2009, Article ID: 270492, 13 p.
[6] Erde’lyi, A., Magnus, W., Oberhettinger F. and Tricomi, F.G. (1954) Tables of Integral Transform. McGraw-Hill, New York.

  
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