Results on Compositions Involving Dirac-delta Function

Ozcag E.

9th International Conference on Promoting the Application of Mathematics in Technical and Natural Sciences (AMiTaNS), Albena, Bulgaria, 21 - 26 June 2017, vol.1895 identifier identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 1895
  • Doi Number: 10.1063/1.5007379
  • City: Albena
  • Country: Bulgaria
  • Hacettepe University Affiliated: Yes

Abstract

The distributional composition delta((r))(x(+)(lambda)) for lambda = 0, in other words, the composition delta((r))(H(X)) is defined as the neutrix limit of the regular sequence {delta((r))(n)(x(+)(lambda))} and the expressions [(delta((r))(x)](-k) and [delta((r))(+)(x)](-k) are defined as a double neutrix limit of the regular sequences [delta((r))(m)(x)](n)(-k) and [(delta((r))(m)(x))(+)](n)(-k) respectively. Further compositions such as H-(r)(delta((s))(x)) and H-lambda(x) are also defined in the neutrix setting.