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...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/750524 |
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| author | S. K. Q. Al-Omari A. Kılıçman |
| author_facet | S. K. Q. Al-Omari A. Kılıçman |
| author_sort | S. K. Q. Al-Omari |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-1fe0cf5e1fc745979f7a73866712e6d4 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-1fe0cf5e1fc745979f7a73866712e6d42025-02-03T05:50:20ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/750524750524Unified Treatment of the Krätzel Transformation for Generalized FunctionsS. K. Q. Al-Omari0A. Kılıçman1Department of Applied Sciences, Faculty of Engineering Technology, Al-Balqa Applied University, Amman 11134, JordanDepartment of Mathematics and Institute of Mathematical Research, Universiti Putra Malaysia (UPM), 43400 Serdang, Selangor, MalaysiaWe 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.http://dx.doi.org/10.1155/2013/750524 |
| spellingShingle | S. K. Q. Al-Omari A. Kılıçman Unified Treatment of the Krätzel Transformation for Generalized Functions Abstract and Applied Analysis |
| 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 kratzel transformation for generalized functions |
| url | http://dx.doi.org/10.1155/2013/750524 |
| work_keys_str_mv | AT skqalomari unifiedtreatmentofthekratzeltransformationforgeneralizedfunctions AT akılıcman unifiedtreatmentofthekratzeltransformationforgeneralizedfunctions |