Asymptotic Expansions of the Wavelet Transform in Rn

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Authors

  • R. S. Pathak
     DST Centre for Interdisciplinary Mathematical Sciences, Banaras Hindu University, Varanasi 221005 ,IN

Keywords:

Asymptotic Expansion, Wavelet Transform, Fourier Transform, Error Bound.
Numerical Analysis

Abstract

Moment asymptotic expansions of the n-dimensional wavelet transform are obtained for large values of the dilation parameter a. Using representation of the n-dimensional wavelet transform as a 2n-dimensional Fourier transform asymptotic expansion of the wavelet transform with explicit error bound is also obtained. Results are illustrated by means of suitable examples.

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Published

2015-12-01

How to Cite

Pathak, R. S. (2015). Asymptotic Expansions of the Wavelet Transform in R<sup>n</sup>. The Journal of the Indian Mathematical Society, 82(3-4), 157–168. Retrieved from https://informaticsjournals.co.in/index.php/jims/article/view/1690

Issue

Volume 82, Issue 3-4, July-December 2015

Section

Articles

License

Copyright (c) 2015 R. S. Pathak

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

 

References

Yu. A. Brychkov and A.P. Prudinkov, Integral Transforms of Generalized Functions, Gordan and Breach Science Pubslishers, Ansterdam, 1989.

C.K. Chui, An Introduction to Wavelets, Academic Press, New York, 1992.

L. Debnath, Wavelet Transforms and Their Applications, Birkhauser, Boston, 2002.

R.Estrada and R. P. Kanwal, A distributional theory for asymptotic expansions, Proc. Roy. Soc. London, Sec.A 428 (1990),399–430.

R. Estrada and R. P. Kanwal, The asymptotic expansion of certain multi-dimensional generalized functions, J. Math. Anal. Appl.. 163(1) (1992), 264–283.

D.S. Jones, Asymptotic behaviour of integrals, SIAM Review, 14 (1972), 286–317.

R. S. Pathak, The Wavelet Transform, Atlantis Press/World Scientific, 2009.

R. S. Pathak, Properties of The Wavelet transform II, Investigations Math. Sci., 4(1) (2004), 45-64.

R. S. Pathak and A. Pathak, Asymptotic expansions of the wavelet transform for large and small values of b, Int. J. Math. Math. Sci., 2009 Article ID 270492, 13 pages.

P. N. Shivakumar and R. Wong, Asymptotic expansion of multiple Fourier transform,, SIAM J. Math. Anal., 10 (1971), 1095–1104.

R.Wong, Asymptotic Approximations of Integrals,Academic Press, New York 1989.

A. I. Zayed, Asymptotic expansions of some integral transforms by using generlized functions, Trans. Amer. Math. Soc., 272 (1982), 785–802.