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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Taylor & Francis
2010
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| Online Access: | http://psasir.upm.edu.my/id/eprint/15912/ 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 |
| _version_ | 1848842812784640000 |
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| author | Fisher, Brian Kilicman, Adem |
| author_facet | Fisher, Brian Kilicman, Adem |
| author_sort | Fisher, Brian |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | 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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| first_indexed | 2025-11-15T08:05:05Z |
| format | Article |
| id | upm-15912 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T08:05:05Z |
| publishDate | 2010 |
| publisher | Taylor & Francis |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-159122015-09-22T03:33:07Z http://psasir.upm.edu.my/id/eprint/15912/ On the composition and neutrix composition of the delta function and powers of the inverse hyperbolic sine function Fisher, Brian Kilicman, Adem 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. Taylor & Francis 2010-12 Article PeerReviewed application/pdf en 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 Fisher, Brian and Kilicman, Adem (2010) On the composition and neutrix composition of the delta function and powers of the inverse hyperbolic sine function. Integral Transforms and Special Functions, 21 (12). pp. 935-944. ISSN 1065-2469; ESSN: 1476-8291 10.1080/10652469.2010.497271 |
| spellingShingle | Fisher, Brian Kilicman, Adem On the composition and neutrix composition of the delta function and powers of the inverse hyperbolic sine function |
| title | On the composition and neutrix composition of the delta function and powers of the inverse hyperbolic sine function |
| title_full | On the composition and neutrix composition of the delta function and powers of the inverse hyperbolic sine function |
| title_fullStr | On the composition and neutrix composition of the delta function and powers of the inverse hyperbolic sine function |
| title_full_unstemmed | On the composition and neutrix composition of the delta function and powers of the inverse hyperbolic sine function |
| title_short | On the composition and neutrix composition of the delta function and powers of the inverse hyperbolic sine function |
| title_sort | on the composition and neutrix composition of the delta function and powers of the inverse hyperbolic sine function |
| url | http://psasir.upm.edu.my/id/eprint/15912/ http://psasir.upm.edu.my/id/eprint/15912/ 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 |