`Abstract and Applied AnalysisVolume 2007, Article ID 81907, 10 pageshttp://dx.doi.org/10.1155/2007/81907`
Research Article

## On the Noncommutative Neutrix Product of Distributions

1Department of Mathematics, University of Hacettepe, Ankara, Beytepe 06532, Turkey
2Faculty of Electrical Engineering, Karpos II bb, Skopje 9100, Macedonia

Received 21 August 2007; Accepted 5 November 2007

Copyright © 2007 Emin Özçaḡ et al. 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.

1. J. G. van der Corput, “Introduction to the neutrix calculus,” Journal d'Analyse Mathématique, vol. 7, pp. 281–399, 1960.
2. R. Hoskins and J. S. Pinto, Distributions Ultradistributions and Other Generalized Functions, Ellis Horwood, Chichester, UK, 1994.
3. B. Fisher, “Neutrices and the product of distributions,” Studia Mathematica, vol. 57, no. 3, pp. 263–274, 1976.
4. B. Fisher, “A non-commutative neutrix product of distributions,” Mathematische Nachrichten, vol. 108, no. 1, pp. 117–127, 1982.
5. B. Fisher and K. Taş, “On the non-commutative neutrix product of the distributions ${x}_{+}^{\lambda }$ and ${x}_{+}^{\mu }$,” Acta Mathematica Sinica, vol. 22, no. 6, pp. 1639–1644, 2006.
6. B. Fisher and K. Taş, “On the non-commutative neutrix product of the distributions ${x}_{+}^{-r}{ln}^{p}{x}_{+}$ and ${x}_{+}^{\mu }{ln}^{q}x$,” Integral Transforms and Special Functions, vol. 17, no. 7, pp. 513–519, 2006.
7. E. Özçaḡ, B. Fisher, and H. Gürçay, “Some results on the non-commutative neutrix product of distributions,” Integral Transforms and Special Functions, vol. 11, no. 1, pp. 49–60, 2001.
8. Y. J. Ng and H. van Dam, “Neutrix calculus and finite quantum field theory,” Journal of Physics A, vol. 38, no. 18, pp. L317–L323, 2005.
9. Y. Jack Ng and H. van Dam, “An application of neutrix calculus to quantum theory,” International Journal of Modern Physics A, vol. 21, no. 2, pp. 297–312, 2006.
10. B. Fisher, “The product of distributions,” The Quarterly Journal of Mathematics, vol. 22, no. 2, pp. 291–298, 1971.
11. B. Fisher, “On defining the product of distributions,” Mathematische Nachrichten, vol. 99, no. 1, pp. 239–249, 1980.
12. B. Fisher and A. Kiliçman, “Neutrices and the non-commutative neutrix product of distributions,” Boletín Sociedad Matemática Mexicana, vol. 3, no. 2, pp. 299–307, 1997.
13. I. M. Gel'fand and G. E. Shilov, Generalized Functions. Vol. I: Properties and Operations, Academic Press, New York, NY, USA, 1964.
14. E. Özçaḡ and B. Fisher, “On defining the distribution ${x}_{+}^{-r}ln{x}_{+}$,” Rostocker Mathematisches Kolloquium, no. 42, pp. 25–30, 1990.