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-invariantH 2 (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 ε 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.
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This research was supported by the National Science Foundation and by the Army Research Office.
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Tadmorf, G. A time-varying Beurling-Lax theorem and a related interpolation problem. Math. Control Signal Systems 7, 148–166 (1994). https://doi.org/10.1007/BF01211471
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DOI: https://doi.org/10.1007/BF01211471