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.

Abstract


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.


Full Text: PDF

 

References


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

  2. Ahmed Fitouhi and M. Moncef Hamza, The q-jαBessel Function, Journal of Approximation Theory 115(2002), 144-166. Google Scholar

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

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

  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. Google Scholar

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

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