Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 482467, 20 pages
http://dx.doi.org/10.1155/2010/482467
Research Article

On the Solution -Dimensional of the Product Operator and Diamond Bessel Operator

Department of Mathematics, Chiangmai University, Chiangmai 50200, Thailand

Received 15 August 2009; Revised 21 November 2009; Accepted 12 January 2010

Academic Editor: Victoria Vampa

Copyright © 2010 Wanchak Satsanit and Amnuay Kananthai. 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. A. Kananthai, “On the solutions of the n-dimensional diamond operator,” Applied Mathematics and Computation, vol. 88, no. 1, pp. 27–37, 1997. View at Publisher · View at Google Scholar · View at MathSciNet
  2. A. Kananthai, “On the diamond operator related to the wave equation,” Nonlinear Analysis: Theory, Methods & Applications, vol. 47, no. 2, pp. 1373–1382, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. H. Yıldırım, M. Z. Sarikaya, and S. Öztürk, “The solutions of the n-dimensional Bessel diamond operator and the Fourier-Bessel transform of their convolution,” Proceedings of Indian Academy of Sciences, vol. 114, no. 4, pp. 375–387, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  4. R. Courant and D. Hilbert, Methods of Mathematical Physics, vol. 2, Interscience, New York, NY, USA, 1966.
  5. Y. Nozaki, “On Riemann-Liouville integral of ultra-hyperbolic type,” Kodai Mathematical Seminar Reports, vol. 16, pp. 69–87, 1964. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. S. E. Trione, “On Marcel Riesz on the ultra-hyperbolic kernel,” Trabajos de Mathematica, vol. 116, pp. 1–12, 1987. View at Google Scholar
  7. W. F. Donoghue, Distributions and Fourier Transform, Academic Press, New York, NY, USA, 1969. View at Zentralblatt MATH
  8. I. M. Gel'fand and G. E. Shilov, Generalized Functions. Vol. I: Properties and Operations, Academic Press, New York, NY, USA, 1964. View at Zentralblatt MATH · View at MathSciNet
  9. M. Zeki Sarikaya and H. Yıldırım, “On the operator Bk related to the Bessel-wave operator and Laplacian-Bessel,” in Advances in Inequality for Special Function, P. Cerone and S. S. Dragomir, Eds., 2008. View at Google Scholar
  10. A. H. Zemanian, Distribution Theory and Transform Analysis. An Introduction to Generalized Functions, with Applications, McGraw-Hill, New York, NY, USA, 1965. View at MathSciNet
  11. M. Z. Sarıkaya and H. Yıldırım, “On the Bessel diamond and the nonlinear Bessel diamond operator related to the Bessel wave equation,” Nonlinear Analysis: Theory, Methods & Applications, vol. 68, no. 2, pp. 430–442, 2008. View at Publisher · View at Google Scholar · View at MathSciNet