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BESSEL-WRIGHT TRANSFORM IN THE SETTING OF QUANTUM CALCULUS

  • Received : 2020.07.11
  • Accepted : 2021.03.25
  • Published : 2021.06.30

Abstract

This work is devoted to the study of a q-harmonic analysis related to the q-analog of the Bessel-Wright integral transform [6]. We establish some important properties of this transform and we focalise our attention in studying the associated transmutation operator.

Keywords

Acknowledgement

The authors would like to thank the anonymous reviewers for their helpful and constructive comments that greatly contributed to improving the final version of the paper.

References

  1. Bouzeffour F., Inversion formulas for q-Riemann-Liouville and q-Weyl transforms, J. Math. Anal. Appl. 336 (2007), 833-848. https://doi.org/10.1016/j.jmaa.2007.01.111
  2. Berkak I., Loualid E.M. and Daher R., An extension of the Bessel-Wright transform in the class of Boehmians. Arab. J. Math. 9 (2020) , 271-280. https://doi.org/10.1007/s40065-019-0250-z.
  3. Dhaouadi L., On the q-Bessel Fourier Transform, Bulletin of Mathematical Analysis and Applications 5 (2013), 42-60.
  4. Dhaouadia L., Binous W., Fitouhi A., Paley-Wiener theorem for the q-Bessel transformand associated q-sampling formula, Expo. Math. 27 (2009), 55-72. https://doi.org/10.1016/j.exmath.2008.07.002
  5. Dhaouadi L., Fitouhi A. and El Kamel J., Inequalities in q-Fourier Analysis, Journal of Inequalities in Pure and Applied Mathematics, 7 (2006), 171.
  6. Fitouhi A., Dhaouadi L. and Karoui I., On the Bessel-Wright Transform. Anal. Math. 45 (2019), 291-309. https://doi.org/10.1007/s10476-018-0659-1
  7. Fitouhi A., Hamza M. and Bouzeffour F., The q-j Bessel function, J. Appr. Theory, 115 (2002), 144-166. https://doi.org/10.1006/jath.2001.3645
  8. Gasmi A. and Sifi M., The Bessel-Struve interwining operator on C and mean periodic functions, IJMMS 59 (2004), 3171-3185.
  9. Gasper G., Rahman M., Basic Hypergeometric Series Encyclopedia of Mathematics and its Application , second ed., vol. 35, Cambridge University Press, Cambridge, UK, (2004).
  10. Hardy G. H., Littlewood J. E., and Polya G., Inequalities, Cambridge University Press, New York (1934).
  11. Karoui I., Binous W., Fitouhi A., On the Bessel-Wright Operator and Transmutation with Applications. In: Kravchenko V., Sitnik S. (eds) Transmutation Operators and Applications. Trends in Mathematics. Birkhauser, Cham (2020). https://doi.org/10.1007/978-3-030-35914-0_18.
  12. Koornwinder T. H., Swarttouw R. F., On q-analogues of the Fourier and Hankel transforms, Trans. Amer. Math. Soc. 333 (1992), 445-461. https://doi.org/10.1090/S0002-9947-1992-1069750-0
  13. Zayed A. I. , Handbook of Function and Generalized Function Transformations, Boca Raton. Fla. CRC Press (1996).