SOME PROPERTIES OF HANKEL CONVOLUTION-OPERATORS

Let H(mu)' be the Zemanian space of Hankel transformable generalized functions and let O(mu,*)' be the space of Hankel convolution operators for H(mu)'. This H(mu)' is the dual of a subspace H(mu) of O(mu,*)' for which O(mu,*)' is also the space of Hankel convolutors. In this paper the elements of O(mu,*)' are characterized as those in L(H(mu)) and in L(H(mu)') that commute with Hankel translations. Moreover, necessary and sufficient conditions on the generalized Hankel transform H(mu)'S of S is-an-element-of O(mu,*)' are established in order that every T is-an-element-of O(mu,*)' such that S * T is-an-element-of H(mu) lie in H(mu).