An Asymptotic Expansion of Continuous Wavelet Transform for Small Dilation Parameter

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Authors

  • Ashish Pathak
     Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi - 221005 ,IN
  • Prabhat Yadav
     Department of Mathematics, NERIST, Nirjuli - 791109 ,IN
  • M. M. Dixit
     Department of Mathematics, NERIST, Nirjuli - 791109 ,IN

DOI:

https://doi.org/10.18311/jims/2022/29311

Keywords:

Asymptotic expansion, Wavelet transform, Fourier transform, Mellin transform

Abstract

In this paper, we derive asymptotic expansion of the wavelet transform for small values of the dilation parameter a by using Lopez and Pagola technique. Asymptotic expansion of Morlet wavelet, Mexican Hat wavelet and Haar wavelet transform are obtained as a special cases.

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Published

2022-01-27

How to Cite

Pathak, A., Yadav, P., & Dixit, M. M. (2022). An Asymptotic Expansion of Continuous Wavelet Transform for Small Dilation Parameter. The Journal of the Indian Mathematical Society, 89(1-2), 134–144. https://doi.org/10.18311/jims/2022/29311

Issue

Volume 89, Issue 1-2, January-June 2022

Section

Articles

License

Copyright (c) 2022 Ashish Pathak, Prabhat Yadav, M. M. Dixit

Creative Commons License

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

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Europe PMC
Received 2022-01-11
Accepted 2023-01-30
Published 2022-01-27

 

References

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R. S. Pathak and Ashish Pathak, Asymptotic expansion of Wavelet Transform for small value a, The Wavelet Transforms, World Scientific, (2009), 164–170. DOI: https://doi.org/10.2991/978-94-91216-24-4_10

R. S. Pathak and Ashish Pathak, Asymptotic expansion of Wavelet Transform with error term, The Wavelet Transforms, World Scientific, (2009), 154–164. DOI: https://doi.org/10.2991/978-94-91216-24-4_9

R. S. Pathak and Ashish Pathak, Asymptotic Expansions of the Wavelet Transform for Large and Small Values of b, Inter. J. Math. Math. Sc., Vol. 2009, 13 pages. DOI: https://doi.org/10.1155/2009/270492

Ashish Pathak, Prabhat Yadav and M. M. Dixit, An asymptotic expansion of continuous wavelet transform for large dilation parameter, Bol. Soc. Parana. Mat. 3 (36) (2018), 27-39. DOI: https://doi.org/10.5269/bspm.v36i3.31221

R.Wong, Explicit error terms for asymptotic expansion of Mellin convolutions, J. Math. Anal. Appl. 72 (1979), 740–756. DOI: https://doi.org/10.1016/0022-247X(79)90261-0

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