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International Journal of Functional Analysis, Operator Theory and Applications

Abstract:
Let F be a distribution and f be a locally summable function. The neutrix composition

of F and f, is defined as the neutrix limit of the sequence

where

and

is a certain sequence of infinitely differentiable functions converging to the Dirac delta-function

It is proved that the neutrix composition of the distributions

and

exists and is equal to

for

and

Keywords and phrases: distribution, delta-function, neutrix composition of distributions, neutrix, neutrix limit.

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