The continuous generalized wavelet transform associated with q-Bessel operator
DOI :
https://doi.org/10.5269/bspm.52810Résumé
The continuous generalized wavelet transform associated with -Bessel operator is defined, which will invariably be called continuous -Bessel wavelet transform . Certain and boundedness results and inversion formula for continuous -Bessel wavelet transform are obtained. Discrete -Bessel wavelet transform is defined and a reconstruction formula is derived for discrete- Bessel wavelet.
Références
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2. G. Kaiser, A Friendly Guide to Wavelets. Birkhauser (1994).
3. R. S. Pathak, Fourier - Jacobi wavelet transform. Vijnana Parishad Anushandhan Patrika, 47, 7-15, (2004).
4. M. M. Dixit, R. Kumar and C.P.Pandey, Generalized wavelet transform associated with Legendre polynomials. International Journal of Computer Applications,108(12),(2014). https://doi.org/10.5120/18966-0308
5. R. S. Pathak and C. P.Pandey, Wavelet transform in Generalized Sobolev space. Journal of Indian Mathematical Society,73,235-247,(2006).
6. R. S. Pathak and C. P.Pandey, Lagurree wavelet transforms. Integral transform and special functions,20, 505-518,(2009). https://doi.org/10.1080/10652460802047809
7. K. Trimeche, Generalized Wavelets and Hypergroups. Gordon and Breach Science Publishers, Amsterdam (1997). https://doi.org/10.1007/978-0-8176-4348-5_12
8. G. Gasper and M. Rahman, Generalized Wavelets and Hypergroups. Basic hypergeometric series, 2nd edn. Cambridge University Press, (2004). https://doi.org/10.1017/CBO9780511526251
9. A. Fitouhi, M. Hamza and F. Bouzeffour, The q − jα Bessel function. J. Approx. Theory,115, 114-116,(2002). https://doi.org/10.1006/jath.2001.3645
10. T. H. Koornwinder and R. F. Swarttouw, On q-Analogues of the Fourier and Hankel transforms. Trans. Amer Math. Soc. 333, 445-461,(1992). https://doi.org/10.1090/S0002-9947-1992-1069750-0
11. A. Fitouhi, L. Dhaouadi and J. El Kamel, Inequalities in q-Fourier analysis.J. Inequal. Pure Appl. Math, 171, 1-14(2006).
12. A. Fitouhi and L. Dhaouadi, Positivity of the generalized translation operator associated to the q-Hankel transform. Constr. Approx,34,453-472 (2011). https://doi.org/10.1007/s00365-011-9132-0
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2022-12-21
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