Linear passive stationary scattering systems with Pontryagin state spaces

✍ Scribed by D. Z. Arov; J. Rovnyak; S. M. Saprikin

• Publisher: John Wiley and Sons
• Year: 2006
• Tongue: English
• Weight: 329 KB
• Volume: 279
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.200410428

✦ Synopsis

Abstract

Passive scattering systems having Pontryagin state spaces and their minimal conservative dilations are investigated. The transfer functions of passive scattering systems are generalized Schur functions. In the case of a simple conservative system, the right and left Kreĭn–Langer factorizations of the transfer function correspond to natural cascade syntheses of systems. A generalization of Sz.–Nagy and Foias criteria for a cascade synthesis of two simple conservative systems to be simple is obtained for systems with Pontryagin state spaces. It is shown that the state space of a simple passive system admits certain unique fundamental decompositions, which give rise to a notion of stability and a characterization of simple conservative systems whose transfer functions have unitary boundary values a.e. on the unit circle. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)