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01-Applied Mathematics & Information Sciences
An International Journal


Volumes > Volume 5 > No. 3


Some Results on the Composition of Singular Distributions

PP: 623-634
Adem Kılıcman, Brian Fisher,
Let F be a distribution in D0 and let f be a locally summable function. The neutrix composition F(f(x)) of F and f is said to exist and equal to the distribution h(x) if the neutrix limit of the sequence fFn(f(x))g is equal to h(x), where Fn(x) = F(x) n(x) for n = 1; 2; : : : and fn(x)g is a certain regular sequence converging to the Dirac delta function. In particular, the composition F(f(x)) is said to exist and be equal to the distribution h if the sequence fFn(f(x))g converges to h in the normal sense. In this study it was proved that if F(x) denotes the distribution x?1, then the composition F(sinh x) exists and given by F(sinh x) = coshec x. Some further similar results are also deduced.

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