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Bessel-Wright transform in the setting of quantum calculus

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

Abstract

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

참고문헌 (13)

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  4. Dhaouadia L., "Paley-Wiener theorem for the q-Bessel transformand associated q-sampling formula", Expo. Math, 27, pp.55~72 (2009)
  5. Dhaouadi L., "Inequalities in q-Fourier Analysis", Journal of Inequal-ities in Pure and Applied Mathematics, 7, pp.171~ (2006)
  6. Fitouhi A., "On the Bessel–Wright Transform", Anal. Math, 45, pp.291~309 (2019)[DOI]
  7. Fitouhi A., "The q-j Bessel function", J. Appr. Theory, 115, pp.144~166 (2002)
  8. Gasmi A., "The Bessel-Struve interwining operator on C and mean periodic functions", IJMMS, 59, pp.3171~3185 (2004)
  9. Gasper G., "Basic Hypergeometric Series Encyclopedia of Mathematics and its Application, vol. 35" (2004), Cambridge University Press
  10. Hardy G. H., "Inequalities" (1934), Cambridge University Press
  11. Karoui I., "Transmutation Operators and Applications. Trends in Mathematics" (2020), Birkh¨auser
  12. Koornwinder T. H., "On q-analogues of the Fourier and Hankel transforms", Trans. Amer. Math. Soc, 333, pp.445~461 (1992)
  13. Zayed A. I., "Handbook of Function and Generalized Function Transformations" (1996), CRC Press

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