Abstract
This article concerns linear time-varying interpretations of the Beurling-Lax-Ball-Helton theorem and of Sarason's interpolation problem. The former characterizes shift-invariantH2 (Krein) subspaces. Unilateral shift invariance reflects both causality and time invariance. Removing the stationarity requirement, a generalized theorem provides a characterization of certain causal subspace families Mt ⊂L2(t, ∞), t e ℝ. Sarason's interpolation problem is interpreted here as a search for a (close to) minimal induced norm system, given causal input-output specifications. The Beurling-Lax theorem helps in identifying admissible specification classes. The problem is then reduced to and solved in terms of a linear time-varying Nehari problem. Technically, developments are based on timedomain, state-space methods.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
