Title: Harmonic Analysis Associated with the Generalized q-Bessel Operator
Author(s): Ahmed Abouelaz, Radouan Daher, El Mehdi Loualid
Pages: 17-23
Cite as:
Ahmed Abouelaz, Radouan Daher, El Mehdi Loualid, Harmonic Analysis Associated with the Generalized q-Bessel Operator, Int. J. Anal. Appl., 10 (1) (2016), 17-23.


In this article, we give a new harmonic analysis associated with the generalized q-Bessel operator. We introduce the generalized $q$-Bessel transform, the generalized q-Bessel translation and the generalized $q$-Bessel convolution product.

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  1. A. Fitouhi and L. Dhaouadi, Positivity of the generalized Translation Associated with the q-Hankel Transform, Constructive Approximation, 34(2011), 435-472.

  2. Ahmed Fitouhi and M. Moncef Hamza, The q-j╬▒Bessel Function, Journal of Approximation Theory 115(2002), 144-166.

  3. F.H. Jackson, On a q-Defnite Integrals, Quarterly Journal of Pure and Application Mathematics, 41(1910), 193-203.

  4. G.Gasper and M.Rahman, Basic hypergeometric series, Encycopedia of mathematics and its applications, Volume 35, Cambridge university press (1990).

  5. L.Dhaouadi, A.Fitouhi and J.El Kamel, Inequalities in q-Fourier Analysis, journal of Inequalities in Pure and Applied Mathematics, 7(2006), Article ID 171.

  6. L.Dhaoudi, On the q-Bessel Fourier transform, Bulletin of Mathematical Analysis and Applications, 5(2013), 42-60.

  7. R. F. Swarttouw, The Hahn-Exton q-Bessel functions, Ph. D. Thesis, Delft Technical University (1992).