Journal of Operator Theory

Volume 58, Issue 1, Summer 2007 pp. 23-38.

On Lax-Phillips semigroups

Authors: Hellmut Baumgaertel
Author institution: University of Potsdam, Mathematical Institute Am Neuen Palais 10, PF 601553, D-14415 Potsdam, Germany

Summary: 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. The basic connection of the Lax-Phillips semigroup to the so-called characteristic semigroup of the reference evolution is emphasized.

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