Properties of the realization of inner functions


Jacob, Birgit and Zwart, Hans (2002) Properties of the realization of inner functions. Mathematics of control, signals, and systems, 15 (4). pp. 356-379. ISSN 0932-4194

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Abstract:In this paper we investigate fundamental properties of state-space realizations for inner functions. We derive necessary and sufficient conditions for the inner function to have a realization such that the associated $C_0$-semigroup is exponentially stable. Furthermore, we give necessary and sufficient conditions on the inner function such that the $C_0$-semigroup is a group. Combining these results, we have that the $C_0$-semigroup is an exponentially stable $C_0$-group if and only if the inner function is the product of a constant of modulus one and a Blaschke product for which the zeros satisfy the Carleson-Newman condition and the zeros lie in a vertical strip bounded away from the imaginary axis.
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Copyright:© 2002 Springer
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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