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Journal of Applied Mathematics
Volume 2011, Article ID 951960, 15 pages
http://dx.doi.org/10.1155/2011/951960
Research Article

On the Diamond Bessel Heat Kernel

Department of Mathematics, Faculty of Science, Maejo University, Chiangmai 50290, Thailand

Received 19 July 2011; Accepted 2 November 2011

Academic Editor: Tak-Wah Lam

Copyright © 2011 Wanchak Satsanit. 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
  2. Y. Nozaki, “On Riemann-Liouville integral of ultra-hyperbolic type,” Kodai Mathematical Seminar Reports, vol. 16, no. 2, pp. 69–87, 1964. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. H. Yildirim, M. Z. Sarikaya, and S. Öztürk, “The solutions of the n-dimensional Bessel diamond operator and the Fourier-Bessel transform of their convolution,” Proceedings Mathematical Sciences, vol. 114, no. 4, pp. 375–387, 2004. View at Publisher · View at Google Scholar
  4. H. Yildirim, Riesz potentials generated by a generalized shift operator, Ph.D. thesis, Ankara University, 1995.
  5. I. A. Kipriyanov, “Boundary value problems for partial differential equations with Bessel's differential operator,” Doklady Akademii Nauk, vol. 158, no. 2, pp. 274–278, 1967. View at Google Scholar
  6. A. Saglam, H. Yildirim, and M. Z. Sarikaya, “On the Bessel ultra-hyperbolic heat equation,” Thai Journal of Mathematics, vol. 8, no. 1, pp. 149–159, 2010. View at Google Scholar · View at Zentralblatt MATH
  7. I. A. Kiprijanov, “Fourier-Bessel transforms and imbedding theorems for weight classes,” Trudy Matematicheskogo Instituta imeni V. A. Steklova, vol. 89, pp. 130–213, 1967. View at Google Scholar
  8. B. M. Levitan, “Expansion in Fourier series and integrals with Bessel functions,” Uspekhi Matematicheskikh Nauk, vol. 6, pp. 102–143, 1951 (Russian). View at Google Scholar
  9. H. Yildirim and A. Sağlam, “On the generalized Bessel heat equation related to the generalized Bessel diamond operator,” Hacettepe Journal of Mathematics and Statistics, vol. 40, no. 2, pp. 179–189, 2011. View at Google Scholar
  10. H. Yildirim, M. Z. Sarikaya, and A. Saglam, “On the Bessel heat equation related to the Bessel diamond operator,” Acta Applicandae Mathematicae, vol. 109, no. 3, pp. 849–860, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH