ON THE COMPOSITION OF THE DISTRIBUTIONS $x^{-1}ln^{m}\lvert x \rvert$ AND $x^r$

Year 2008, Volume: 37 Issue: 1, 1 - 8, 01.01.2008

Brian Fisher İnci Ege Emin Özçağ

Abstract

Let F be a distribution and f a locally summable function. The distribution $F(f)$ is defined as the neutrix limit of the sequence $\{Fn(f)\}$, where $F_n(x)=F(x)*\delta_{n}(x)$ and $\{delta_{n}(x)\}$ is a certain sequence of infinitely differentiable functions converging to the Dirac delta-function $\delta(x)$. The composition of the distributions $x^{-1}ln^{m}\lvert x \rvert$ and $x^r$ is evaluated for r,m = 1, 2, 3 . . ..

Keywords

Distribution, Delta-function, Composition of distributions, Neutrix, Neu- trix limit

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