On the Composition of Distributions x − s ln | x | and | x | μ

Biljana Jolevska-Tuneska and Emin Özça¯g

International Journal of Mathematics and Mathematical Sciences, 2007, vol. 2007, 1-9

Abstract:

Let F be a distribution and let f be a locally summable function. The distribution F ( f ) is defined as the neutrix limit of the sequence { F n ( f ) } , where F n ( x ) = F ( x ) * δ n ( x ) and { δ n ( x ) } is a certain sequence of infinitely differentiable functions converging to the Dirac delta-function δ ( x ) . The composition of the distributions x − s In | x | and | x | μ is evaluated for s = 1 , 2 , … , μ > 0 and μ s ≠1 , 2 , … .

Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:060129

DOI: 10.1155/2007/60129

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