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Keywords:
multipliers; generalized functions; Hankel transformation
multipliers; generalized functions; Hankel transformation
Summary:
\font\jeden=rsfs10 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 $\text{\jeden O}$, 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.
References:
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