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An Asymptotic Expansion of Continuous Wavelet Transform for Small Dilation Parameter
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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.
Keywords
Asymptotic expansion, Wavelet transform, Fourier transform, Mellin transform.
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- A. Erdlyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Tables of Integral Transforms, 1. McGraw-Hill, New York, 1954.
- Jos L. Lopez and Pedro Pagola, Asymptotic expansions of Mellin convolution integrals: An oscillatory case, J. Computational Appl. Math., 233 (2010), 1562-1569.
- R. S. Pathak, Wavelet Transforms, World scientific, 2009.
- R. S. Pathak and Ashish Pathak, Asymptotic expansion of Wavelet Transform for small value a, The Wavelet Transforms, World Scientific, (2009), 164–170.
- R. S. Pathak and Ashish Pathak, Asymptotic expansion of Wavelet Transform with error term, The Wavelet Transforms, World Scientific, (2009), 154–164.
- 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.
- 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.
- R.Wong, Explicit error terms for asymptotic expansion of Mellin convolutions, J. Math. Anal. Appl. 72 (1979), 740–756.
- R. Wong, Asymptotic Approximations of Integrals, Academic Press, New York, 1989.
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