System Theory, Operator Models and Scattering: The Time-Varying Case

Document Type

Article

Publication Date

2002

Abstract

It is well known that linear system theory, Lax-Phillips scattering theory, and operator model theory for a contraction operator are all intimately related. A common thread in all three theories is a contractive, analytic, operator-valued function on the unit disk W(z) having a representation of the form W(z) = D + zC(I − zA)−1B, known, depending on the context, as the transfer function, the scattering function, or the characteristic function. We present the time-varing analogue of this framework. Also included is a time-varying analogue of the Abstract Interpolation Problem of Katsnelson-Kheifets-Yuditskii.

Comments

This article was originally published in Journal of Operator Theory, volume 47, in 2002.

Peer Reviewed

1

Copyright

American Mathematical Society

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