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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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