Partial multiplication of operators in rigged Hilbert spaces

The problem of the multiplication of operators acting in riggedHilbert spaces is considered. This is done, as usual, by constructing certainintermediate spaces through which the product can be factorized. In the specialcase where the starting space is the set of analytic vectors of a self-adjointoperator A, a general procedure for constructing a special family of interspacesis given. Their definition closely reminds that of the Bessel potentialspaces, to which they reduce when the starting space is the Schwartz space. Some applications are considered.