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: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Publishing Corporation
2013
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| 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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| Summary: | 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. |
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