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A result on the composition of distributions

  • Joel D. Nicholas
  • Brian Fisher
Article

Abstract

LetF be a distribution and letf be a locally summable function. The distributionF(f) is defined as the neutrix limit of the sequenceF n (f), whereF n (x) = F(x) * δ n (x) andδ n (x) is a certain sequence of infinitely differentiable functions converging to the Dirac delta-functionδ(x). The distribution (xr)−s is valuated forr, s = 1,2, ….

Keywords

Distribution delta-function composition of distributions neutrix neutrix limit 

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References

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    van der Corput J G, Introduction to the neutrix calculus,J. Anal. Math. 7 (1959) 291–398CrossRefGoogle Scholar
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    Fisher B, On defining the distribution δ(r) (f(x)), Rostock. Math. Kolloq. 23 (1993) 73–80Google Scholar
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    Fisher B, On defining the change of variable in distributions,Rostock. Math. Kolloq. 28 (1985) 75–86MATHGoogle Scholar
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    Fisher B, On defining the distribution (x+r −s,Univ. u Novom Sadu Zb. Rad. Prirod.-Mat. Fak. Ser. Mat. 15 (1985) 119–129MATHMathSciNetGoogle Scholar
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    Gel’fand I M and Shilov G E,Generalized Functions, Vol. I, Academic Press (1964)Google Scholar

Copyright information

© Indian Academy of Science 1999

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceUniversity of LeicesterLeicesterEngland

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