Continuous and Discrete Wavelet Transforms Associated with Hermite Transform
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Abstract
In this paper, we accomplished the concept of continuous and discrete Hermite wavelet transforms. We also discussed some basic properties of Hermite wavelet transform. Inversion formula and Parsevals formula for continuous Hermite wavelet transform is established. Moreover the discrete version of wavelet transform is discussed.
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References
- A. Pathak, Abhishek, Wavelet transforms associated with the Index Whittaker transform, ArXiv:1908.03766 [Math]. 2019.
- C. Markett, The Product Formula and Convolution Structure Associated with the Generalized Hermite Polynomials, J. Approx. Theory, 73 (1993) 199-217.
- H. Glaeske, Convolution structure of (generalized) Hermite transforms, Algebra Analysis and related topics, Banach Center Publications, Vol 53 (1), 113-120 (2000).
- A. Prasad, U.K. Mandal, Wavelet transforms associated with the Kontorovich-Lebedev transform, Int. J. Wavelets Multiresolut Inf. Process. 15 (2017) 1750011.
- R.S. Pathak, C.P. Pandey, Laguerre wavelet transforms, Integral Transforms Spec. Funct. 20 (2009), 505-518.
- R.S. Pathak, M.M. Dixit, Continuous and discrete Bessel wavelet transforms, J. Comput. Appl. Math. 160 (12) (2003), 241-250.
- S.K. Upadhyay, A. Tripathi, Continuous Watson wavelet transform, Integral Transforms Spec. Funct. 23 (2012), 639-647.
- C.K. Chui, An introduction to wavelets, Academic Press, New York, 1992.
- E.C. Titchmarch, Introduction to theory of Fourier integrals, 2nd edition, Oxford University Press, Oxford, U.K. 1948.