Unified treatment of the Krätzel transformation for generalized functions
We discuss a generalization of the Krätzel transforms on certain spaces of ultradistributions. We have proved that the Krätzel transform of an ultradifferentiable function is an ultradifferentiable function and satisfies its Parseval's inequality. We also provide a complete reading of the trans...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Hindawi Publishing Corporation
2013
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| Online Access: | http://psasir.upm.edu.my/id/eprint/30130/ http://psasir.upm.edu.my/id/eprint/30130/1/30130.pdf |
| _version_ | 1848846590944477184 |
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| author | Al-Omari, Shrideh Khalaf Qasem Kilicman, Adem |
| author_facet | Al-Omari, Shrideh Khalaf Qasem Kilicman, Adem |
| author_sort | Al-Omari, Shrideh Khalaf Qasem |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | We discuss a generalization of the Krätzel transforms on certain spaces of ultradistributions. We have proved that the Krätzel transform of an ultradifferentiable function is an ultradifferentiable function and satisfies its Parseval's inequality. We also provide a complete reading of the transform constructing two desired spaces of Boehmians. Some other properties of convergence and continuity conditions and its inverse are also discussed in some detail. |
| first_indexed | 2025-11-15T09:05:08Z |
| format | Article |
| id | upm-30130 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T09:05:08Z |
| publishDate | 2013 |
| publisher | Hindawi Publishing Corporation |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-301302017-10-19T06:01:35Z http://psasir.upm.edu.my/id/eprint/30130/ Unified treatment of the Krätzel transformation for generalized functions Al-Omari, Shrideh Khalaf Qasem Kilicman, Adem We discuss a generalization of the Krätzel transforms on certain spaces of ultradistributions. We have proved that the Krätzel transform of an ultradifferentiable function is an ultradifferentiable function and satisfies its Parseval's inequality. We also provide a complete reading of the transform constructing two desired spaces of Boehmians. Some other properties of convergence and continuity conditions and its inverse are also discussed in some detail. Hindawi Publishing Corporation 2013 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/30130/1/30130.pdf Al-Omari, Shrideh Khalaf Qasem and Kilicman, Adem (2013) Unified treatment of the Krätzel transformation for generalized functions. Abstract and Applied Analysis, 2013. art. no. 750524. pp. 1-7. ISSN 1085-3375; ESSN: 1687-0409 https://www.hindawi.com/journals/aaa/2013/750524/abs/ 10.1155/2013/750524 |
| spellingShingle | Al-Omari, Shrideh Khalaf Qasem Kilicman, Adem Unified treatment of the Krätzel transformation for generalized functions |
| title | Unified treatment of the Krätzel transformation for generalized functions |
| title_full | Unified treatment of the Krätzel transformation for generalized functions |
| title_fullStr | Unified treatment of the Krätzel transformation for generalized functions |
| title_full_unstemmed | Unified treatment of the Krätzel transformation for generalized functions |
| title_short | Unified treatment of the Krätzel transformation for generalized functions |
| title_sort | unified treatment of the krätzel transformation for generalized functions |
| url | http://psasir.upm.edu.my/id/eprint/30130/ http://psasir.upm.edu.my/id/eprint/30130/ http://psasir.upm.edu.my/id/eprint/30130/ http://psasir.upm.edu.my/id/eprint/30130/1/30130.pdf |