ABSTRACT

A way of utilizing Lax-Phillips type semigroups for the description of time evolution of resonances for scattering problems involving Hamiltonians with a semibounded spectrum was recently introduced by the author. In the proposed framework the evolution is decomposed into a background term and an exponentially decaying resonance term evolving according to a semigroup law given by a Lax-Phillips type semigroup; this is called the semigroup decomposition.