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Results on the Neutrix Composition of the Delta Function

Year 2007, Volume: 36 Issue: 2, 147 - 156, 01.02.2007

References

  • van der Corput, J. G. Introduction to the neutrix calculus, J. Analyse Math. 7, 291–398, Fisher, B. On defining the distribution δ(r)(f (x)), Rostock. Math. Kolloq. 23, 73–80, 1983.
  • Fisher, B. On defining the change of variable in distributions, Rostock. Math. Kolloq. 28, –40, 1985.
  • Fisher, B. The delta function and the composition of distributions, Dem. Math. 35 (1), –123, 2002.
  • Fisher, B. The composition and neutrix composition of distributions, in: Kenan Ta¸s, et al. (Eds.) (Mathematical Methods in Engineering, Springer, Dordrecht, 2007, pp. 59–69).
  • Fisher, B. and Jolevska-Tuneska, B. Two results on the composition of distributions, Thai. J. Math. 3 (1), 17–26, 2005.
  • Fisher, B., Jolevska-Tuneska, B. and ¨Oz¸ca¯g, E. Further results on the composition of dis- tributions, Integral Transforms Spec. Funct. 13 (2),109–116, 2002.
  • Fisher,B., Kananthai, A., Sritanatana, G. and Nonlaopon, K. The composition of the dis- tributions xmsln x−and x − r−p/m + , Integral Transforms Spec. Funct. 16 (1), 13–20, 2005.
  • Fisher, B. and Ta¸s, K. On the composition of the distributions x−rand xµ, Indian J. Pure + + Appl. Math. 36 (1), 11–22, 2005.
  • Fisher, B. and Ta¸s, K. On the composition of the distributions x−1ln |x| and xr,Integral + Transforms Spec. Funct. 16 (7), 533–543, 2005.
  • Fisher, B. and Ta¸s, K. On the composition of the distributions xλand xµ, J. Math. Anal. ++ Appl. 318 (1), 102–111, 2006.
  • Gel’fand, I. M. and Shilov, G. E. Generalized Functions, Volume 1 (Academic Press, New York and London, 1st edition, 1964).
  • Koh, E. L. and Li, C. K. On Distributions δkand(δ0)k,Math. Nachr. 157, 243–248, 1992.
  • Kou, H. and Fisher, B. On Composition of Distributions, Publ. Math. Debrecen 40 (3-4), –290, 1992.
  • ¨Oz¸ca¯g, Emin Defining the kth Powers of the Dirac Delta Distribution for Negative Integers, Appl. Math. Letters 14, 419–423, 2001.
  • ¨Oz¸ca¯g, E., Ege, I. and G¨ur¸cay, H. On Powers of the Heaviside Function for negative integers, J. Math. Anal. Appl. 326, 101–107, 2007.

Results on the Neutrix Composition of the Delta Function

Year 2007, Volume: 36 Issue: 2, 147 - 156, 01.02.2007

References

  • van der Corput, J. G. Introduction to the neutrix calculus, J. Analyse Math. 7, 291–398, Fisher, B. On defining the distribution δ(r)(f (x)), Rostock. Math. Kolloq. 23, 73–80, 1983.
  • Fisher, B. On defining the change of variable in distributions, Rostock. Math. Kolloq. 28, –40, 1985.
  • Fisher, B. The delta function and the composition of distributions, Dem. Math. 35 (1), –123, 2002.
  • Fisher, B. The composition and neutrix composition of distributions, in: Kenan Ta¸s, et al. (Eds.) (Mathematical Methods in Engineering, Springer, Dordrecht, 2007, pp. 59–69).
  • Fisher, B. and Jolevska-Tuneska, B. Two results on the composition of distributions, Thai. J. Math. 3 (1), 17–26, 2005.
  • Fisher, B., Jolevska-Tuneska, B. and ¨Oz¸ca¯g, E. Further results on the composition of dis- tributions, Integral Transforms Spec. Funct. 13 (2),109–116, 2002.
  • Fisher,B., Kananthai, A., Sritanatana, G. and Nonlaopon, K. The composition of the dis- tributions xmsln x−and x − r−p/m + , Integral Transforms Spec. Funct. 16 (1), 13–20, 2005.
  • Fisher, B. and Ta¸s, K. On the composition of the distributions x−rand xµ, Indian J. Pure + + Appl. Math. 36 (1), 11–22, 2005.
  • Fisher, B. and Ta¸s, K. On the composition of the distributions x−1ln |x| and xr,Integral + Transforms Spec. Funct. 16 (7), 533–543, 2005.
  • Fisher, B. and Ta¸s, K. On the composition of the distributions xλand xµ, J. Math. Anal. ++ Appl. 318 (1), 102–111, 2006.
  • Gel’fand, I. M. and Shilov, G. E. Generalized Functions, Volume 1 (Academic Press, New York and London, 1st edition, 1964).
  • Koh, E. L. and Li, C. K. On Distributions δkand(δ0)k,Math. Nachr. 157, 243–248, 1992.
  • Kou, H. and Fisher, B. On Composition of Distributions, Publ. Math. Debrecen 40 (3-4), –290, 1992.
  • ¨Oz¸ca¯g, Emin Defining the kth Powers of the Dirac Delta Distribution for Negative Integers, Appl. Math. Letters 14, 419–423, 2001.
  • ¨Oz¸ca¯g, E., Ege, I. and G¨ur¸cay, H. On Powers of the Heaviside Function for negative integers, J. Math. Anal. Appl. 326, 101–107, 2007.
There are 15 citations in total.

Details

Primary Language Turkish
Journal Section Mathematics
Authors

B. Fisher This is me

T. Kraiweeradechachai This is me

E. Özçağ This is me

Publication Date February 1, 2007
Published in Issue Year 2007 Volume: 36 Issue: 2

Cite

APA Fisher, B., Kraiweeradechachai, T., & Özçağ, E. (2007). Results on the Neutrix Composition of the Delta Function. Hacettepe Journal of Mathematics and Statistics, 36(2), 147-156.
AMA Fisher B, Kraiweeradechachai T, Özçağ E. Results on the Neutrix Composition of the Delta Function. Hacettepe Journal of Mathematics and Statistics. February 2007;36(2):147-156.
Chicago Fisher, B., T. Kraiweeradechachai, and E. Özçağ. “Results on the Neutrix Composition of the Delta Function”. Hacettepe Journal of Mathematics and Statistics 36, no. 2 (February 2007): 147-56.
EndNote Fisher B, Kraiweeradechachai T, Özçağ E (February 1, 2007) Results on the Neutrix Composition of the Delta Function. Hacettepe Journal of Mathematics and Statistics 36 2 147–156.
IEEE B. Fisher, T. Kraiweeradechachai, and E. Özçağ, “Results on the Neutrix Composition of the Delta Function”, Hacettepe Journal of Mathematics and Statistics, vol. 36, no. 2, pp. 147–156, 2007.
ISNAD Fisher, B. et al. “Results on the Neutrix Composition of the Delta Function”. Hacettepe Journal of Mathematics and Statistics 36/2 (February 2007), 147-156.
JAMA Fisher B, Kraiweeradechachai T, Özçağ E. Results on the Neutrix Composition of the Delta Function. Hacettepe Journal of Mathematics and Statistics. 2007;36:147–156.
MLA Fisher, B. et al. “Results on the Neutrix Composition of the Delta Function”. Hacettepe Journal of Mathematics and Statistics, vol. 36, no. 2, 2007, pp. 147-56.
Vancouver Fisher B, Kraiweeradechachai T, Özçağ E. Results on the Neutrix Composition of the Delta Function. Hacettepe Journal of Mathematics and Statistics. 2007;36(2):147-56.