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Multipliers of Hankel transformable generalized functions. (English) Zbl 0801.46047
Summary: Let \({\mathcal H}_ \mu\) be the Zemanian space of Hankel transformable functions, and let \({\mathcal H}_ \mu'\) be its dual space. In this paper \({\mathcal H}_ \mu\) is shown to be nuclear, hence Schwartz, Montel and reflexive. The space \({\mathcal O}\), also introduced by Zemanian, is completely characterized as the set of multipliers of \({\mathcal H}_ \mu\) and of \({\mathcal H}_ \mu'\). Certain topologies are considered on \({\mathcal O}\), and continuity properties of the multiplication operation with respect to those topologies are discussed.

MSC:
46F12 Integral transforms in distribution spaces
46F10 Operations with distributions and generalized functions
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