Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2013, Article ID 841585, 7 pages
http://dx.doi.org/10.1155/2013/841585
Research Article

On the Generalized Krätzel Transform and Its Extension to Bohemian Spaces

1Department of Applied Sciences, Faculty of Engineering Technology, Al-Balqa Applied University, Amman 11134, Jordan
2Department of Mathematics and Institute of Mathematical Research, University of Putra Malaysia (UPM), 43400 Serdang, Selangor, Malaysia

Received 4 September 2013; Accepted 12 November 2013

Academic Editor: Mohammad Mursaleen

Copyright © 2013 S. K. Q. Al-Omari and Adem Kılıçman. 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, “Unified treatment of the Krätzel transformation for generalized functions,” Abstract and Applied Analysis, vol. 2013, Article ID 750524, 7 pages, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. E. Krätzel, “Eine Verallgemeinerung der Laplace- und Meijer-Transformation,” Wissenschaftliche Zeitschrift der Friedrich-Schiller, vol. 14, pp. 369–381, 1965. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. D. I. Cruz-Báez and J. Rodríguez, “The Lν(ρ)-transformation on McBride's spaces of generalized functions,” Commentationes Mathematicae Universitatis Carolinae, vol. 39, no. 3, pp. 445–452, 1998. View at Google Scholar · View at MathSciNet
  4. G. L. N. Rao and L. Debnath, “A generalized Meijer transformation,” International Journal of Mathematics and Mathematical Sciences, vol. 8, no. 2, pp. 359–365, 1985. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. A. H. Zemanian, Generalized Integral Transformations, Dover, New York, NY, USA, 2nd edition, 1987. View at MathSciNet
  6. V. Karunakaran and R. A. Chella Rajathi, “Gelfand transform for a Boehmian space of analytic functions,” Annales Polonici Mathematici, vol. 101, no. 1, pp. 39–45, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. J. Beardsley and P. Mikusiński, “A sheaf of Boehmians,” Annales Polonici Mathematici, vol. 107, no. 3, pp. 293–307, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. D. Nemzer, “One-parameter groups of Boehmians,” Bulletin of the Korean Mathematical Society, vol. 44, no. 3, pp. 419–428, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. P. Mikusiński, “Fourier transform for integrable Boehmians,” The Rocky Mountain Journal of Mathematics, vol. 17, no. 3, pp. 577–582, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. P. Mikusiński, “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 Zentralblatt MATH · View at MathSciNet
  11. P. Mikusiński, “Convergence of Boehmians,” Japanese Journal of Mathematics, vol. 9, no. 1, pp. 159–179, 1983. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. S. K. Q. Al-Omari and A. Kılıçman, “On generalized Hartley-Hilbert and Fourier-Hilbert transforms,” Advances in Difference Equations, vol. 2012, article 232, 12 pages, 2012. View at Google Scholar
  13. 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 Zentralblatt MATH · View at MathSciNet
  14. D. Nemzer, “Boehmians on the torus,” Bulletin of the Korean Mathematical Society, vol. 43, no. 4, pp. 831–839, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. V. Karunakaran and C. Ganesan, “Fourier transform on integrable Boehmians,” Integral Transforms and Special Functions, vol. 20, no. 11-12, pp. 937–941, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. 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 Zentralblatt MATH · View at MathSciNet
  17. D. Nemzer, “A note on the convergence of a series in the space of Boehmians,” Bulletin of Pure and Applied Mathematics, vol. 2, no. 1, pp. 63–69, 2008. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet