Published in

Taylor and Francis Group, Integral Transforms and Special Functions, 12(21), p. 935-944

DOI: 10.1080/10652469.2010.497271

Links

Tools

Export citation

Search in Google Scholar

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

Journal article published in 2010 by Brian Fisher, Adem Kilicman ORCID
This paper was not found in any repository, but could be made available legally by the author.
This paper was not found in any repository, but could be made available legally by the author.

Full text: Unavailable

Red circle
Preprint: archiving forbidden
Orange circle
Postprint: archiving restricted
Red circle
Published version: archiving forbidden
Data provided by SHERPA/RoMEO

Abstract

Lets F be a distribution in D' and let f be a locally summable function. The composition F(f(x)) of F and f is said to exist and be equal to the distribution h(x) if the limit of the sequence {Fn(f(x))} is equal to h(x), where Fn(x)=F(x)*δn(x) for n=1, 2, … and {δn(x)} is a certain regular sequence converging to the Dirac delta function. It is proved that the neutrix composition δ[(sinh x+)] exists and for s=0, 1, 2, … and r=1, 2, …, where M is the smallest integer greater than (s−r +1)/r and Further results are also proved.