[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.11568/kjm.2021.29.2.253

BESSEL-WRIGHT TRANSFORM IN THE SETTING OF QUANTUM CALCULUS

Karoui, Ilyes (Faculte des Sciences de Tunis)
Dhaouadi, Lazhar (I.P.E.Bizerte)
Binous, Wafa (Institut preparatoire aux etudes d'ingenieurs de Tunis)
Haddad, Meniar (Faculte des Sciences de Tunis)

Publication Information

Korean Journal of Mathematics / v.29, no.2, 2021 , pp. 253-266 More about this Journal

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

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

Citations & Related Records

Reference

1	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 DOI
2	Fitouhi A., Hamza M. and Bouzeffour F., The q-j Bessel function, J. Appr. Theory, 115 (2002), 144-166. DOI
3	Gasmi A. and Sifi M., The Bessel-Struve interwining operator on C and mean periodic functions, IJMMS 59 (2004), 3171-3185.
4	Gasper G., Rahman M., Basic Hypergeometric Series Encyclopedia of Mathematics and its Application , second ed., vol. 35, Cambridge University Press, Cambridge, UK, (2004).
5	Hardy G. H., Littlewood J. E., and Polya G., Inequalities, Cambridge University Press, New York (1934).
6	Koornwinder T. H., Swarttouw R. F., On q-analogues of the Fourier and Hankel transforms, Trans. Amer. Math. Soc. 333 (1992), 445-461. DOI
7	Zayed A. I. , Handbook of Function and Generalized Function Transformations, Boca Raton. Fla. CRC Press (1996).
8	Bouzeffour F., Inversion formulas for q-Riemann-Liouville and q-Weyl transforms, J. Math. Anal. Appl. 336 (2007), 833-848. DOI
9	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. DOI
10	Dhaouadi L., On the q-Bessel Fourier Transform, Bulletin of Mathematical Analysis and Applications 5 (2013), 42-60.
11	Dhaouadia L., Binous W., Fitouhi A., Paley-Wiener theorem for the q-Bessel transformand associated q-sampling formula, Expo. Math. 27 (2009), 55-72. DOI
12	Dhaouadi L., Fitouhi A. and El Kamel J., Inequalities in q-Fourier Analysis, Journal of Inequalities in Pure and Applied Mathematics, 7 (2006), 171.
13	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.