A result on the composition of distributions

  • Joel D. Nicholas
  • Brian Fisher


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, ….


Distribution delta-function composition of distributions neutrix neutrix limit 


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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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