Unified treatment of the Kratzel transformation for generalized functions
Al-Omari, Shrideh Khalaf Qasem and Kilicman, Adem (2013) Unified treatment of the Kratzel transformation for generalized functions. Abstract and Applied Analysis, 2013 . art. no. 750524. pp. 1-7. ISSN 1085-3375; ESSN: 1687-0409
Official URL: http://dx.doi.org/10.1155/2013/750524
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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