Resonances as Eigenvalues in the Gelʼfand Triplet Approach for Finite-Dimensional Friedrichs Models on the Positive Half Line

Abstract

The eigenvalue problem for the resonances of finite-dimensional Friedrichs models on the positive half line is solved using an appropriate Gelʼfand triplet. The associated Gamow vectors are uniquely determined by the corresponding eigenantilinear forms. They turn out to be the restriction of the eigenantilinear forms to the Hardy space part of the Gelʼfand space. Conditions are presented such that there are only finitely many resonances and all resonances are simple poles of the scattering matrix.