A comparison on the commutative neutrix convolution of distributions and the exchange formula
Let f̃, g̃ be ultradistributions in ℒ' and let f̃n = f̃ * δn and g̃n = g̃ * σn where {δn} is a sequence in ℒ which converges to the Dirac-delta function δ. Then the neutrix product f̃ ◇ g̃ is defined on the space of ultradistributions ℒ' as the neutrix limit of the sequence {1/2(f̃ng̃ + f̃...
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| Format: | Article |
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Institute of Mathematics, Czech Academy of Sciences
2001
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| Online Access: | http://psasir.upm.edu.my/id/eprint/115212/ |
| _version_ | 1848866715863089152 |
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| author | Kiliçman, Adem |
| author_facet | Kiliçman, Adem |
| author_sort | Kiliçman, Adem |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | Let f̃, g̃ be ultradistributions in ℒ' and let f̃n = f̃ * δn and g̃n = g̃ * σn where {δn} is a sequence in ℒ which converges to the Dirac-delta function δ. Then the neutrix product f̃ ◇ g̃ is defined on the space of ultradistributions ℒ' as the neutrix limit of the sequence {1/2(f̃ng̃ + f̃g̃n)} provided the limit h̃ exist in the sense that N-limn→∞1/2〈f̃ng̃ + f̃g̃n, ψ〉 = 〈h̃, ψ〉 for all ψ in ℒ. We also prove that the neutrix convolution product f g exist in' , if and only if the neutrix product f tild; ◇ g̃ exist in ℒ and the exchange formula F(f g) = f̃ ◇ g̃ is then satisfied. |
| first_indexed | 2025-11-15T14:25:01Z |
| format | Article |
| id | upm-115212 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-15T14:25:01Z |
| publishDate | 2001 |
| publisher | Institute of Mathematics, Czech Academy of Sciences |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-1152122025-02-26T06:08:42Z http://psasir.upm.edu.my/id/eprint/115212/ A comparison on the commutative neutrix convolution of distributions and the exchange formula Kiliçman, Adem Let f̃, g̃ be ultradistributions in ℒ' and let f̃n = f̃ * δn and g̃n = g̃ * σn where {δn} is a sequence in ℒ which converges to the Dirac-delta function δ. Then the neutrix product f̃ ◇ g̃ is defined on the space of ultradistributions ℒ' as the neutrix limit of the sequence {1/2(f̃ng̃ + f̃g̃n)} provided the limit h̃ exist in the sense that N-limn→∞1/2〈f̃ng̃ + f̃g̃n, ψ〉 = 〈h̃, ψ〉 for all ψ in ℒ. We also prove that the neutrix convolution product f g exist in' , if and only if the neutrix product f tild; ◇ g̃ exist in ℒ and the exchange formula F(f g) = f̃ ◇ g̃ is then satisfied. Institute of Mathematics, Czech Academy of Sciences 2001 Article PeerReviewed Kiliçman, Adem (2001) A comparison on the commutative neutrix convolution of distributions and the exchange formula. Czechoslovak Mathematical Journal, 51 (3). pp. 463-471. ISSN 0011-4642, 1572-9141 https://link.springer.com/article/10.1023/A:1013719619356?error=cookies_not_supported&code=fa5b77d0-1c48-49d8-a2e8-95ba7c29ee8e 10.1023/A:1013719619356 |
| spellingShingle | Kiliçman, Adem A comparison on the commutative neutrix convolution of distributions and the exchange formula |
| title | A comparison on the commutative neutrix convolution of distributions and the exchange formula |
| title_full | A comparison on the commutative neutrix convolution of distributions and the exchange formula |
| title_fullStr | A comparison on the commutative neutrix convolution of distributions and the exchange formula |
| title_full_unstemmed | A comparison on the commutative neutrix convolution of distributions and the exchange formula |
| title_short | A comparison on the commutative neutrix convolution of distributions and the exchange formula |
| title_sort | comparison on the commutative neutrix convolution of distributions and the exchange formula |
| url | http://psasir.upm.edu.my/id/eprint/115212/ http://psasir.upm.edu.my/id/eprint/115212/ http://psasir.upm.edu.my/id/eprint/115212/ |