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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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Main Authors: Al-Omari, Shrideh Khalaf Qasem, Kilicman, Adem
Format: Article
Language:English
Published: Hindawi Publishing Corporation 2013
Online Access:http://psasir.upm.edu.my/id/eprint/30130/1/30130.pdf
http://psasir.upm.edu.my/id/eprint/30130/
https://www.hindawi.com/journals/aaa/2013/750524/abs/
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spelling my.upm.eprints.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
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/
language English
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
author Al-Omari, Shrideh Khalaf Qasem
Kilicman, Adem
spellingShingle Al-Omari, Shrideh Khalaf Qasem
Kilicman, Adem
Unified treatment of the Krätzel transformation for generalized functions
author_facet Al-Omari, Shrideh Khalaf Qasem
Kilicman, Adem
author_sort Al-Omari, Shrideh Khalaf Qasem
title Unified treatment of the Krätzel transformation for generalized functions
title_short 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_sort unified treatment of the krätzel transformation for generalized functions
publisher Hindawi Publishing Corporation
publishDate 2013
url http://psasir.upm.edu.my/id/eprint/30130/1/30130.pdf
http://psasir.upm.edu.my/id/eprint/30130/
https://www.hindawi.com/journals/aaa/2013/750524/abs/
_version_ 1643829966559772672
score 13.18916

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