Abstract:Let $\Cal H_{\mu }$ be the Zemanian space of Hankel transformable functions, and let $\Cal H'_{\mu }$ be its dual space. In this paper $\Cal H_{\mu }$ is shown to be nuclear, hence Schwartz, Montel and reflexive. The space $\Cal O$, also introduced by Zemanian, is completely characterized as the set of multipliers of $\Cal H_{\mu }$ and of $\Cal H'_{\mu }$. Certain topologies are considered on $\Cal O$, and continuity properties of the multiplication operation with respect to those topologies are discussed.
Keywords: multipliers, generalized functions, Hankel transformation
AMS Subject Classification: Primary 46F12