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Journal of Mathematics
Volume 2014, Article ID 790161, 5 pages
http://dx.doi.org/10.1155/2014/790161
Research Article

Some Definition of Hartley-Hilbert and Fourier-Hilbert Transforms in a Quotient Space of Boehmians

Department of Applied Sciences, Faculty of Engineering Technology, Al-Balqa’ Applied University, Amman 11134, Jordan

Received 20 May 2014; Accepted 16 August 2014; Published 6 November 2014

Academic Editor: Tepper L Gill

Copyright © 2014 S. K. Q. Al-Omari. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. S. K. Q. Al-Omari and A. Kılıçman, “Some remarks on the extended Hartley-Hilbert and Fourier-Hilbert transforms of boehmians,” Abstract and Applied Analysis, vol. 2013, Article ID 348701, 6 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  2. N. Sundararajan and Y. Srinivas, “Fourier-Hilbert versus Hartley-Hilbert transforms with some geophysical applications,” Journal of Applied Geophysics, vol. 71, no. 4, pp. 157–161, 2010. View at Publisher · View at Google Scholar · View at Scopus
  3. R. P. Millane, “Analytical properties of the Hartley transform and their implications,” Proceedings of the IEEE, vol. 82, no. 3, pp. 413–428, 1994. View at Publisher · View at Google Scholar · View at Scopus
  4. S. K. Al-Omari and A. Kılıçman, “On diffraction Fresnel transforms for Boehmians,” Abstract and Applied Analysis, vol. 2011, Article ID 712746, 11 pages, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. S. K. Al-Omari, “Hartley transforms on a certain space of generalized functions,” Georgian Mathematical Journal, vol. 20, no. 3, pp. 415–426, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. S. K. Q. Al-Omari and A. Kilicman, “On the generalized Hartley-Hilbert and Fourier-Hilbert transforms,” Advances in Difference Equations, vol. 2012, article 232, 2012. View at Publisher · View at Google Scholar
  7. T. K. Boehme, “The support of Mikusiński operators,” Transactions of the American Mathematical Society, vol. 176, pp. 319–334, 1973. View at Google Scholar · View at MathSciNet
  8. R. Roopkumar, “Mellin transform for Boehmians,” Bulletin of the Institute of Mathematics: Academia Sinica: New Series, vol. 4, no. 1, pp. 75–96, 2009. View at Google Scholar · View at MathSciNet
  9. R. Roopkumar, “Generalized Radon transform,” Rocky Mountain Journal of Mathematics, vol. 36, no. 4, pp. 1375–1390, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. P. Mikusinski and A. Zayed, “The Radon transform of Boehmians,” Proceedings of the American Mathematical Society, vol. 118, no. 2, pp. 561–570, 1993. View at Publisher · View at Google Scholar · View at MathSciNet
  11. S. K. Al-Omari and A. Kilicman, “Note on Boehmians for class of optical Fresnel wavelet transforms,” Journal of Function Spaces and Applications, vol. 2021, Article ID 405368, 14 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  12. V. Karunakaran and R. Vembu, “Hilbert transform on periodic boehmians,” Houston Journal of Mathematics, vol. 29, no. 2, pp. 437–454, 2003. View at Google Scholar · View at MathSciNet · View at Scopus
  13. V. Karunakaran and R. Roopkumar, “Operational calculus and Fourier transform on Boehmians,” Colloquium Mathematicum, vol. 102, no. 1, pp. 21–32, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  14. S. K. 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 and Special Functions, vol. 19, no. 6, pp. 453–462, 2008. View at Google Scholar · View at MathSciNet · View at Scopus
  15. P. Mikusinski, “Tempered Boehmians and ultradistributions,” Proceedings of the American Mathematical Society, vol. 123, no. 3, pp. 813–817, 1995. View at Publisher · View at Google Scholar · View at MathSciNet
  16. R. S. Pathak, Integral Transforms of Generalized Functions and Their Applications, Gordon and Breach Science, Amsterdam, The Netherlands, 1997. View at MathSciNet