## 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 Strauss. 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. However, the proposed framework assumes that the S -matrix in the energy representation is the boundary value on the positive real axis of a bounded analytic function in the upper half-plane. This condition puts strong restrictions on possible applications of this formalism. In this paper it is shown that there is a simple way of weakening the assumptions on the S -matrix analyticity while still obtaining the semigroup decomposition of the evolution of a resonance.

Original language | English |
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Article number | 102109 |

Journal | Journal of Mathematical Physics |

Volume | 46 |

Issue number | 10 |

DOIs | |

State | Published - 1 Oct 2005 |

Externally published | Yes |

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics