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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Date received: January 11, 1999. Date revised: May 16, 2002.
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ID="*"This paper was supported by the Volkswagen Stiftung (RiP program at Oberwolfach) and by the Deutsche Forschungsgemeinschaft.
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Jacob, B., Zwart, H. Properties of the Realization of Inner Functions. Math. Control Signals Systems 15, 356–379 (2002). https://doi.org/10.1007/s004980200015
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DOI: https://doi.org/10.1007/s004980200015