The composition and neutrix composition of distributions

  • Brian Fisher

Abstract

Let F be a distribution in \( \mathcal{D}' \) and let f be a locally summable function. The neutrix composition F(f(x)) is said to exist and be equal to the distribution h if the neutrix limit of the sequence {F n(f(x))} is h, where F n(x) = F(x)*δ n(x) for n = 1, 2, . . . and {δ n(x)} is a certain regular sequence converging to the Dirac delta funcion. In particular, the composition F(f(x)) is said to exist and be equal to the distribution h if the sequence {F n(f(x))} converges to h in the normal sense. Some results are proved.

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Copyright information

© Springer 2007

Authors and Affiliations

  • Brian Fisher
    • 1
  1. 1.Department of MathematicsUniversity of LeicesterLeicesterUK

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