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Unified treatment of the Krätzel transformation for generalized functions. (English) Zbl 1286.46045

Summary: We discuss a generalization of the Krätzel transforms on certain spaces of ultradistributions. We prove that the Krätzel transform of an ultradifferentiable function is an ultradifferentiable function and satisfies the Parseval 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.

MSC:

46F12 Integral transforms in distribution spaces
46F05 Topological linear spaces of test functions, distributions and ultradistributions
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