International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 270492, 13 pages
Research Article

Asymptotic Expansions of the Wavelet Transform for Large and Small Values of b

Department of Mathematics, Banaras Hindu University, Varanasi 221 005, India

Received 27 July 2009; Accepted 9 September 2009

Academic Editor: A. Zayed

Copyright © 2009 R. S. Pathak and Ashish Pathak. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Asymptotic expansions of the wavelet transform for large and small values of the translation parameter b are obtained using asymptotic expansions of the Fourier transforms of the function and the wavelet. Asymptotic expansions of Mexican hat wavelet transform, Morlet wavelet transform, and Haar wavelet transform are obtained as special cases. Asymptotic expansion of the wavelet transform has also been obtained for small values of b when asymptotic expansions of the function and the wavelet near origin are given.