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ON COMPOSITION OF DISTRIBUTIONS
Last modified: 2014-03-13
Abstract
Let $F$ be a distribution and let $f$ be a locallysummable function. The distribution $F(f)$ is defined as theneutrix limit of the sequence $\left\{F_n(f)\right\}\,,$ where$F_n(x)=F(x)*\delta_n(x)$ and $\left\{\delta_n(x)\right\}$ is acertain sequence of infinitely differentiable functions convergingto the Dirac delta-function $\delta(x).$ Some composition of thedistributions are proved to exists.
Keywords
Distribution, delta-function, composition of distributions, neutrix, neutrix limit