• AL-OMARI, S.K.Q. ;
  • Received : 2014.10.29
  • Published : 2015.09.30


We investigate some generalization of a class of Hankel-Clifford transformations having Fox H-function as part of its kernel on a class of Boehmians. The generalized transform is a one-to-one and onto mapping compatible with the classical transform. The inverse Hankel-Clifford transforms are also considered in the sense of Boehmians.


Hankel transform;Hankel-Clifford transform;Bessel-Clifford function;Fox H-function;Boehmians


  1. S. K. Q. Al-Omari, On the distributional Mellin transformation and its extension to Boehmian spaces, Int. J. Contemp. Math. Sci. 6 (2011), no. 17-20, 801-810.
  2. S. K. Q. Al-Omari, A Mellin transform for a space of Lebesgue integrable Boehmians, Int. J. Contemp. Math. Sci. 6 (2011), no. 29-32, 1597-1606.
  3. S. K. Q. Al-Omari, Distributional and tempered distributional diffraction Fresnel transforms and their extension to Boehmian spaces, Ital. J. Pure Appl. Math. 30 (2013), 179-194.
  4. S. K. Q. Al-Omari, A note on $F^b_a$ transformation of generalized functions, Int. J. Pure Appl. Math. 86 (2013), no. 1, 19-33.
  5. S. K. Q. Al-Omari, Hartley transforms on certain space of generalized functions, Georgian Math. J. (2013) (To Appear).
  6. S. K. Q. Al-Omari, On the application of natural transforms, Int. J. Pure Appl. Math. 85 (2013), no. 4, 729-744.
  7. S. K. Q. Al-Omari and J. F. Al-Omari, Hartley transform for L p Boehmians and spaces of ultradistributions, Int. Math. Forum 7 (2012), 433-443.
  8. S. K. Q. Al-Omari and A. Kilicman, On diffraction Fresnel transforms for Boehmians, Abstr. Appl. Anal. 2011 (2011), Article ID 712746, 11 pp.
  9. S. K. Q. Al-Omari and A. Kilicman, Note on Boehmians for class of optical Fresnel wavelet transforms, J. Function Spaces Appl. 2012 (2012), Article ID 405368, 14 pp.
  10. S. K. Q. Al-Omari and A. Kilicman, On generalized Hartley-Hilbert and Fourier-Hilbert transforms, Adv. Difference Equ. 2012 (2012), no. 232; doi:10.1186/1687-1847-2012-232, 1-12.
  11. S. K. Q. Al-Omari and A. Kilicman, An estimate of Sumudu transform for Boehmians, Adv. Difference Equ. 2013 (2013), no. 77, 10 pp.
  12. S. K. Q. Al-Omari and A. Kilicman, Unified treatment of the Kratzel transformation for generalized functions, Abstr. Appl. Anal. 2013 (2013), Article ID 750524, 7 pp.
  13. S. K. Q. Al-Omari and A. Kilicman, Some remarks on the extended Hartley-Hilbert and Fourier-Hilbert transforms of Boehmians, Abstr. Appl. Anal. 2013 (2013), Article ID 348701, 6 pp.
  14. S. K. Q. Al-Omari, D. Loonker, P. K. Banerji, and S. L. Kalla, Fourier sine (cosine) transform for ultradistributions and their extensions to tempered and ultraBoehmian spaces, Integral Transforms Spec. Funct. 19 (2008), no. 5-6, 453-462.
  15. J. Beardsley and P. Mikusinski, A Sheaf of Boehmians, Ann. Polon. Math. 107 (2013), no. 3, 293-307.
  16. R. Bhuvaneswari and V. Karunakaran, Boehmians of type S and their Fourier transforms, Ann. Univ. Mariae Curie-Sklodowska Sect. A 64 (2010), no. 1, 27-43.
  17. T. K. Boehme, The support of Mikusinski operators, Trans. Amer. Math. Soc. 176 (1973), 319-334.
  18. C. Fox, The G and H functions as symmetrical Fourier kernels, Trans. Amer. Math. Soc. 98 (1961), 395-429.
  19. C. Ganesan, Weighted ultra distributions and Boehmians, Int. J. Math. Anal. 4 (2010), no. 15, 703-712.
  20. V. Karunakaran and C. P. Devi, The Laplace transform on a Boehmian space, Ann. Polon. Math. 97 (2010), no. 2, 151-157.
  21. V. Karunakaran and C. Ganesan, Fourier transform on integrable Boehmians, Integral Transforms Spec. Funct. 20 (2009), no. 11-12, 937-941.
  22. D. Loonker and P. K. Banerji, Wavelet transform of fractional integrals for integrable Boehmians, Appl. Appl. Math. 5 (2010), no. 1, 1-10.
  23. D. Loonker, P. K. Banerji, and L. Debnath, On the Hankel transform for Boehmians, Integral Trasforms Spec. Funct. 21 (2010), no. 7, 479-486.
  24. S. P. Malgonde, Real inversion formula for the generalized Hankel-Clifford transformation, Indian J. Pure Appl. Math. 29 (1998), no. 6, 641-656.
  25. S. P. Malgonde and S. R. Bandewar, On the generalized Hankel-Clifford transformation of arbitrary order, Proc. Indian Acad. Sci. Math. Sci. 110 (2000), no. 3, 293-304.
  26. A. M. Mathai, R. K. Saxena, and H J. Haubold, The H-Function: Theory and Applications, Springer Science+Business Media, LLC, 2010.
  27. P. Mikusinski, Convergence of Boehmians, Japan. J. Math. 9 (1983), no. 1, 159-179.
  28. P. Mikusinski, Fourier transform for integrable Boehmians, Rocky Mountain J. Math. 17 (1987), no. 3, 577-582.
  29. P. Mikusinski, Tempered Boehmians and ultradistributions, Proc. Amer. Math. Soc. 123 (1995), no. 3, 813-817.
  30. D. Nemzer, The Laplace transform on a class of Boehmians, Bull. Austral. Math. Soc. 46 (1992), no. 2, 347-352.
  31. D. Nemzer, One-parameter groups of Boehmians, Bull. Korean Math. Soc. 44 (2007), no. 3, 419-428.
  32. D. Nemzer, A note on the convergence of a series in the space of Boehmians, Bull. Pure Appl. Math. 2 (2008), no. 1, 63-69.
  33. D. Nemzer, A note on multipliers for integrable Boehmians, Fract. Calc. Appl. Anal. 12 (2009), no. 1, 87-96.
  34. D. Nemzer, S-asymptotic properties of Boehmians, Integral Transforms Spec. Funct. 21 (2010), no. 7, 503-513.
  35. R. S. Pathak, Integral Transforms of Generalized Functions and their Applications, Gordon and Breach Science Publishers, Australia, Canada, India, Japan, 1997.
  36. R. Roopkumar, An extension of distributional wavelet transform, Colloq. Math. 115 (2009), no. 2, 195-206.

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Supported by : National Research Foundation of Korea