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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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Main Author: Kiliçman, Adem
Format: Article
Published: Institute of Mathematics, Czech Academy of Sciences 2001
Online Access:http://psasir.upm.edu.my/id/eprint/115212/
https://link.springer.com/article/10.1023/A:1013719619356?error=cookies_not_supported&code=fa5b77d0-1c48-49d8-a2e8-95ba7c29ee8e
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spelling my.upm.eprints.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
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
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.
format Article
author Kiliçman, Adem
spellingShingle Kiliçman, Adem
A comparison on the commutative neutrix convolution of distributions and the exchange formula
author_facet Kiliçman, Adem
author_sort Kiliçman, Adem
title 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_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_sort comparison on the commutative neutrix convolution of distributions and the exchange formula
publisher Institute of Mathematics, Czech Academy of Sciences
publishDate 2001
url http://psasir.upm.edu.my/id/eprint/115212/
https://link.springer.com/article/10.1023/A:1013719619356?error=cookies_not_supported&code=fa5b77d0-1c48-49d8-a2e8-95ba7c29ee8e
_version_ 1825162450806243328
score 13.244413

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