Inversion Formula for the Wavelet Transform on Abelian Group
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Abstract
In this paper a reconstruction and inversion formula of the continuous wavelet transform on abelian group for band-limited function is defined. This formula possesses a more explicit expression than the well-known result. Also, Parseval and other interesting results on abelian group are obtained.
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References
- M. Holschneider, Wavelet Analysis Over Abelian Groups, Appl. Comput. Harmon. Anal. 2 (1995), 52–60. https://doi.org/10.1006/acha.1995.1004.
- C.P. Pandey, P. Phukan, Continuous and Discrete Wavelet Transforms Associated With Hermite Transform, Int. J. Anal. Appl. 18 (2020), 531-549. https://doi.org/10.28924/2291-8639-18-2020-531.
- A. Pathak, P. Yadav, M.M. Dixit, On Convolution for General Novel Fractional Wavelet Transform, arXiv:1404.7682 (2014). https://doi.org/10.48550/ARXIV.1404.7682.
- R.S. Pathak, C.P. Pandey, Laguerre Wavelet Transforms, Integral Transforms Spec. Funct. 20 (2009), 505–518. https://doi.org/10.1080/10652460802047809.
- C.P. Pandey, Jyoti Saikia, The Continuous Wavelet Transform for a q-Bessel Type Operator, Int. J. Anal. Appl., 20 (2022), 33. https://doi.org/10.28924/2291-8639-20-2022-33
- M.M. Dixit, C.P. Pandey, Deepanjan Das, Generalized Continuous Wavelet Transform on Locally Compact Abelian Group, Adv. Inequal. Appl. 2019 (2019), 10. https://doi.org/10.28919/aia/4067.
- C.K. Chui, An Introduction to Wavelets, Academic Press, 1992.
- L. Debnath, The Wavelet Transform and Its Basic Properties, in: Wavelet Transforms and Their Applications, Birkhäuser Boston, Boston, MA, 2002: pp. 361-402. https://doi.org/10.1007/978-1-4612-0097-0_6.