On the Noncommutative Neutrix Product of Distributions
Let f and g be distributions and let gn=(g*δn)(x), where δn(x) is a certain sequence converging to the Dirac-delta function δ(x). The noncommutative neutrix product f∘g of f and g is defined to be the neutrix limit of the sequence {fgn}, provided the limit h exists in the sense that N‐limn→∞〈f...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2007-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2007/81907 |
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| _version_ | 1832551371442749440 |
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| author | Emin Özçaḡ İnci Ege Haşmet Gürçay Biljana Jolevska-Tuneska |
| author_facet | Emin Özçaḡ İnci Ege Haşmet Gürçay Biljana Jolevska-Tuneska |
| author_sort | Emin Özçaḡ |
| collection | DOAJ |
| description | Let f
and g
be distributions and let gn=(g*δn)(x), where δn(x) is a certain sequence converging to the Dirac-delta function δ(x).
The noncommutative neutrix product f∘g
of f
and g
is defined to be the neutrix limit of the sequence {fgn}, provided the limit h
exists in the sense that N‐limn→∞〈f(x)gn(x),φ(x)〉=〈h(x),φ(x)〉, for all test functions in 𝒟. In this paper, using the concept of the neutrix limit due to van der Corput (1960), the noncommutative neutrix products x+rlnx+∘x−−r−1lnx−
and x−−r−1lnx−∘x+rlnx+ are proved to exist and are evaluated for r=1,2,…. It is consequently seen that these two products are in fact equal. |
| format | Article |
| id | doaj-art-0c1888ffadb64848acf1fcf6b4880823 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-0c1888ffadb64848acf1fcf6b48808232025-02-03T06:01:32ZengWileyAbstract and Applied Analysis1085-33751687-04092007-01-01200710.1155/2007/8190781907On the Noncommutative Neutrix Product of DistributionsEmin Özçaḡ0İnci Ege1Haşmet Gürçay2Biljana Jolevska-Tuneska3Department of Mathematics, University of Hacettepe, Ankara, Beytepe 06532, TurkeyDepartment of Mathematics, University of Hacettepe, Ankara, Beytepe 06532, TurkeyDepartment of Mathematics, University of Hacettepe, Ankara, Beytepe 06532, TurkeyFaculty of Electrical Engineering, Karpos II bb, Skopje 9100, MacedoniaLet f and g be distributions and let gn=(g*δn)(x), where δn(x) is a certain sequence converging to the Dirac-delta function δ(x). The noncommutative neutrix product f∘g of f and g is defined to be the neutrix limit of the sequence {fgn}, provided the limit h exists in the sense that N‐limn→∞〈f(x)gn(x),φ(x)〉=〈h(x),φ(x)〉, for all test functions in 𝒟. In this paper, using the concept of the neutrix limit due to van der Corput (1960), the noncommutative neutrix products x+rlnx+∘x−−r−1lnx− and x−−r−1lnx−∘x+rlnx+ are proved to exist and are evaluated for r=1,2,…. It is consequently seen that these two products are in fact equal.http://dx.doi.org/10.1155/2007/81907 |
| spellingShingle | Emin Özçaḡ İnci Ege Haşmet Gürçay Biljana Jolevska-Tuneska On the Noncommutative Neutrix Product of Distributions Abstract and Applied Analysis |
| title | On the Noncommutative Neutrix Product of Distributions |
| title_full | On the Noncommutative Neutrix Product of Distributions |
| title_fullStr | On the Noncommutative Neutrix Product of Distributions |
| title_full_unstemmed | On the Noncommutative Neutrix Product of Distributions |
| title_short | On the Noncommutative Neutrix Product of Distributions |
| title_sort | on the noncommutative neutrix product of distributions |
| url | http://dx.doi.org/10.1155/2007/81907 |
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