On the composition and neutrix composition of the delta function and powers of the inverse hyperbolic sine function

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On the Neutrix Composition of the Delta and Inverse Hyperbolic Sine Functions

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A Result on the Neutrix Composition of the Delta Function

The neutrix composition F (f(x))) of a distribution F (x) and a locally summable function f(x) is said to exist and be equal to the distribution h(x) if the neutrix limit of the sequence {Fn(f(x))} is equal to h(x), where Fn(x) = F (x) ∗ δn(x) and {δn(x)} is a certain sequence of infinitely differentiable functions converging to the Dirac delta-function δ(x). It is proved that the neutrix compo...

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ژورنال

عنوان ژورنال: Integral Transforms and Special Functions

سال: 2010

ISSN: 1065-2469,1476-8291

DOI: 10.1080/10652469.2010.497271