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International Journal of Mathematics and Mathematical Sciences
Volume 2013, Article ID 918905, 5 pages
http://dx.doi.org/10.1155/2013/918905
Research Article

Further Results on Colombeau Product of Distributions

1Faculty of Electrical Engineering and Informational Technologies, Saints Cyril and Methodius University of Skopje, Karpos II bb, 1000 Skopje, Macedonia
2Faculty of Computer Sciences, Goce Delčev University of Štip, Krste Misirkov, Br 10A, 2000 Štip, Macedonia

Received 10 August 2012; Revised 28 November 2012; Accepted 10 December 2012

Academic Editor: Shyam Kalla

Copyright © 2013 Biljana Jolevska-Tuneska and Tatjana Atanasova-Pacemska. 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. Gasiorawics, Elementary Particle Physics, John Wiley & Sons, New York, NY, USA, 1966.
  2. M. Oberguggenberger, Multiplication of Distributions and Application to Partial Differential Equations, vol. 259 of Pitman Research Notes in Mathematics Series, Longman, 1992.
  3. H. König, “Neue Begründung der theorie der distributions,” Mathematische Nachrichten, vol. 9, pp. 129–148, 1953. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. P. Antosik, J. Mikusinski, and R. Sigorski, theory of Distributions. The Sequential Approach, Elsevier, Amsterdam, The Netherlands, 1973.
  5. B. Fisher, “The product of distributions,” The Quarterly Journal of Mathematics, vol. 22, pp. 291–298, 1971. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. B. Fisher, “A noncommutative neutrix product of distributions,” Mathematische Nachrichten, vol. 108, pp. 117–127, 1982. View at Publisher · View at Google Scholar · View at MathSciNet
  7. L. Z. Cheng and B. Fisher, “Several products of distributions on Rm,” Proceedings of the Royal Society London A, vol. 426, no. 1871, pp. 425–439, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. A. H. Zemanian, Distribution Theory and Transform Analysis, Dover, 1965.
  9. I. M. Gel'fand and G. E. Shilov, Generalized Functions, vol. 1, chapter 1, Academic Press, New York, NY, USA, 1964. View at MathSciNet
  10. J.-F. Colombeau, New Generalized Functions and Multiplication of Distributions, vol. 84 of North-Holland Mathematics Studies, North-Holland, Amsterdam, The Netherlands, 1984. View at Zentralblatt MATH · View at MathSciNet
  11. B. Jolevska-Tuneska, A. Takači, and E. Ozcag, “On differential equations with nonstandard coefficients,” Applicable Analysis and Discrete Mathematics, vol. 1, no. 1, pp. 276–283, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  12. B. Damyanov, “Results on Colombeau product of distributions,” Commentationes Mathematicae Universitatis Carolinae, vol. 38, no. 4, pp. 627–634, 1997. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. B. Damyanov, “Some distributional products of Mikusiński type in the Colombeau algebra G(Rm),” Journal of Analysis and its Applications, vol. 20, no. 3, pp. 777–785, 2001. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. B. Damyanov, “Modelling and products of singularities in Colombeau's algebra G(R),” Journal of Applied Analysis, vol. 14, no. 1, pp. 89–102, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. J. Mikusiński, “On the square of the Dirac delta-distribution,” Bulletin de l'Académie Polonaise des Sciences, vol. 14, pp. 511–513, 1966. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet