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A result on the composition of distributions

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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, ….

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Leicester, LE1 7RH, Leicester, England

    Joel D. Nicholas & Brian Fisher

Authors
  1. Joel D. Nicholas
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  2. Brian Fisher
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Correspondence to Joel D. Nicholas.

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Nicholas, J.D., Fisher, B. A result on the composition of distributions. Proc. Indian Acad. Sci. (Math. Sci.) 109, 317–323 (1999). https://doi.org/10.1007/BF02843535

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  • DOI: https://doi.org/10.1007/BF02843535

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