Korean J. Math.  Vol 29, No 2 (2021)  pp.253-266
DOI: https://doi.org/10.11568/kjm.2021.29.2.253

Bessel-Wright transform in the setting of quantum calculus

Ilyes Karoui, Lazhar Dhaouadi, Wafa Binous, Meniar Haddad


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.


q-Harmonic Analysis; q-Bessel-Wright function; q-Bessel-Wright transform; q-Hardy transform

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Bouzeffour F., Inversion formulas for q-Riemann-Liouville and q-Weyl transforms, J. Math. Anal. Appl. 336 (2007), 833–848. (Google Scholar)

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. (Google Scholar)

Dhaouadi L., On the q-Bessel Fourier Transform, Bulletin of Mathematical Analysis and Appli- cations 5 (2013), 42–60. (Google Scholar)

Dhaouadia L., Binous W., Fitouhi A., Paley-Wiener theorem for the q-Bessel transformand associated q-sampling formula, Expo. Math. 27 (2009), 55–72. (Google Scholar)

Dhaouadi L., Fitouhi A. and El Kamel J., Inequalities in q-Fourier Analysis, Journal of Inequal- ities in Pure and Applied Mathematics, 7 (2006), 171. (Google Scholar)

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 (Google Scholar)

Fitouhi A., Hamza M. and Bouzeffour F., The q-j Bessel function, J. Appr. Theory, 115 (2002), 144–166. (Google Scholar)

Gasmi A. and Sifi M., The Bessel-Struve interwining operator on C and mean periodic functions, IJMMS 59 (2004), 3171–3185. (Google Scholar)

Gasper G., Rahman M., Basic Hypergeometric Series Encyclopedia of Mathematics and its Application , second ed., vol. 35, Cambridge University Press, Cambridge, UK, (2004). (Google Scholar)

Hardy G. H., Littlewood J. E., and Polya G., Inequalities, Cambridge University Press, New York (1934). (Google Scholar)

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. Birkh ̈auser, Cham (2020). https://doi.org/10.1007/978-3-030-35914- 0 18. (Google Scholar)

Koornwinder T. H., Swarttouw R. F., On q-analogues of the Fourier and Hankel transforms, Trans. Amer. Math. Soc. 333 (1992), 445–461. (Google Scholar)

Zayed A. I. , Handbook of Function and Generalized Function Transformations, Boca Raton. Fla. CRC Press (1996). (Google Scholar)


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