Abstract
In this paper, we accomplished the concept of convolution of Legendre transform for the study of continuous Legendre wavelet transform. We also presented some discussion on its basic properties such as linearity, shift property, scaling property, symmetry, and parity. Finally, our main goal is to find out the Plancherel and inversion formula for the Continuous Legendre Wavelet Transform (CLWT).
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References
Chui CK (1992) An introduction of wavelets. Academic Press
Cholewinski FM, Haimo DT (1969) The dual Poisson-Laguerre transform. Trans Am Math Soc 144:271–300
Erdèlyi A (ed) (1954) Tables of integral transforms, vol II. McGraw-Hill Book Co., NewYork
Gorlich E, Market C (1982) A convolution structure for Laguerre series. Indag Math 44:61–171
Kaiser G (1994) A friendly guide to wavelets. BirkhauserVerlag, Boston
Pathak RS, Pandey CP (2009) Laguerre wavelet transforms. Integral Transform Spec Funct 20(7):505–518
Pathak RS, Dixit MM (2003) Continuous and discrete Bessel wavelet transforms. J Comput Appl Math 160(12):241–250
Upadhyay SK, Tripathi A. Continuous Watson wavelet transform. Integral Transf Spec Funct 23(9):639–647
Pandey CP, Dixit MM (2014) Generalized wavelet transform associated with legendre polynomials. Int J Comput Appl (0975–8887) 108(12)
Singh VK, Singh OP (2008) Numerical evaluation of the Hankel transform by using linear Legendre multi-wavelets. Comput Phys Commun 179(16):424–429
Trime’che K (1997) Generalized wavelet and hypergroups. Gordon and Breach, Amsterdam
Pathak RS (2009) The wavelet transform. Atlantis Press, Amsterdam, Paris
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Saikia, J., Pandey, C.P. (2021). Inversion Formula for the Wavelet Transform Associated with Legendre Transform. In: Giri, D., Buyya, R., Ponnusamy, S., De, D., Adamatzky, A., Abawajy, J.H. (eds) Proceedings of the Sixth International Conference on Mathematics and Computing. Advances in Intelligent Systems and Computing, vol 1262. Springer, Singapore. https://doi.org/10.1007/978-981-15-8061-1_23
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DOI: https://doi.org/10.1007/978-981-15-8061-1_23
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