2004/10/13 by Hellmut Baumgaertel, Baumgaertel, Hellmut
Mathematics · Physics and Astronomy · #47D06 #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #math-ph #math.MP #msc:47D06
paper · pdf · doi:10.48550/arxiv.math-ph/0410036
16 pages
arxiv created 2004/10/13 · openalex publication_date 2004/10/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Lax-Phillips evolutions are described by two-space scattering systems. The canonical identification operator is characterized for Lax-Phillips evolutions, whose outgoing and incoming projections commute. In this case a (generalized) Lax-Phillips semigroup can be introduced and its spectral theory is considered. In the special case, originally considered by Lax and Phillips (where the outgoing and incoming subspaces are mutually orthogonal), this semigroup coincides with that introduced by Lax and Phillips. In the more general case the existence of the semigroup is not coupled with the (global) holomorphic continuability of the scattering matrix into the upper half plane. The basic connection of the Lax-Phillips semigroup to the so-called characteristic semigroup of the reference evolution is emphasized.