On the composition and neutrix composition of the delta function and powers of the inverse hyperbolic sine function
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 sequ...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Taylor & Francis
2010
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| Online Access: | http://psasir.upm.edu.my/id/eprint/15912/1/On%20the%20composition%20and%20neutrix%20composition%20of%20the%20delta%20function%20and%20powers%20of%20the%20inverse%20hyperbolic%20sine%20function.pdf http://psasir.upm.edu.my/id/eprint/15912/ |
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| Summary: | 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.
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