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MCSS
2008
Springer

Lax-Phillips scattering theory and well-posed linear systems: a coordinate-free approach

8 years 2 months ago
Lax-Phillips scattering theory and well-posed linear systems: a coordinate-free approach
Abstract. We give a further elaboration of the fundamental connections between Lax-Phillips scattering, conservative input/state/output linear systems and Sz.-Nagy-Foias model theory for both the discrete- and continuous-time settings. In particular, for the continuous-time setting, we show how to locate a scattering-conservative L2-well-posed linear system (in the sense of Staffans and Weiss) embedded in a Lax-Phillips scattering system presented in axiomatic form; conversely, given a scattering-conservative linear system, we show how one can view the space of finite-energy input-state-output trajectories of the system as the ambient space for an associated Lax-Phillips scattering system. We use these connections to give a simple, conceptual proof of the identity of the scattering function of the scattering system with the transfer function of the input-state-output linear system. As an application we show how system-theoretic ideas can be used to arrive at the spectral analysis of th...
Joseph A. Ball, Philip T. Carroll, Yoichi Uetake
Added 13 Dec 2010
Updated 13 Dec 2010
Type Journal
Year 2008
Where MCSS
Authors Joseph A. Ball, Philip T. Carroll, Yoichi Uetake
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