On the Composition of Distributions x−sln|x| and |x|μ
Let F be a distribution and let f be a locally summable function. The distribution F(f) is defined as the neutrix limit of the sequence {Fn(f)}, 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). The compositio...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2007-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2007/60129 |
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doaj-f3c2ae1d79d8406697a979df2a67d3442020-11-24T23:49:56ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252007-01-01200710.1155/2007/6012960129On the Composition of Distributions x−sln|x| and |x|μBiljana Jolevska-Tuneska0Emin Özça¯g1Faculty of Electrical Engineering and Information Technologies, Ss. Cyril and Methodius University – Skopje, Karpos II bb, Skopje 1000, MacedoniaDepartment of Mathematics,, Faculty of Science, University of Hacettepe, Beytepe, Ankara 06532, TurkeyLet F be a distribution and let f be a locally summable function. The distribution F(f) is defined as the neutrix limit of the sequence {Fn(f)}, 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). The composition of the distributions x−sIn|x| and |x|μ is evaluated for s=1,2,…,μ>0 and μs≠1,2,….http://dx.doi.org/10.1155/2007/60129 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Biljana Jolevska-Tuneska Emin Özça¯g |
| spellingShingle |
Biljana Jolevska-Tuneska Emin Özça¯g On the Composition of Distributions x−sln|x| and |x|μ International Journal of Mathematics and Mathematical Sciences |
| author_facet |
Biljana Jolevska-Tuneska Emin Özça¯g |
| author_sort |
Biljana Jolevska-Tuneska |
| title |
On the Composition of Distributions x−sln|x| and |x|μ |
| title_short |
On the Composition of Distributions x−sln|x| and |x|μ |
| title_full |
On the Composition of Distributions x−sln|x| and |x|μ |
| title_fullStr |
On the Composition of Distributions x−sln|x| and |x|μ |
| title_full_unstemmed |
On the Composition of Distributions x−sln|x| and |x|μ |
| title_sort |
on the composition of distributions x−sln|x| and |x|μ |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2007-01-01 |
| description |
Let F be a distribution and let f be a locally
summable function. The distribution F(f) is defined as the neutrix limit of the sequence {Fn(f)}, 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). The composition of the distributions x−sIn|x| and |x|μ is evaluated for s=1,2,…,μ>0 and μs≠1,2,…. |
| url |
http://dx.doi.org/10.1155/2007/60129 |
| work_keys_str_mv |
AT biljanajolevskatuneska onthecompositionofdistributionsxslnxandxm AT eminozcag onthecompositionofdistributionsxslnxandxm |
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1725480771890708480 |