Abstract
We define a pair of Gel’fand triplets Φi ⊆ℋi⊆Φ′i, i=1,2, where the linear spaces Φi are formed by suitably chosen entire analytic functions on the Riemann surface associated to the transformation ω=z2. Virtual scattering states are well defined as pairs of functionals, respectively, in Φ1 and Φ′2.