Abstract
A construction is made of a unitary linear system whose transfer function is a given power seriesB(z) with operator coefficients such that multiplication byB(z) is an everywhere defined transformation in the space of square summable power series with vector coefficients. A condition is also given for the existence of an observable linear system with such a transfer function. For both constructions properties of the spaces are given which imply essential uniqueness of linear systems with given transfer functions. A canonical conjugate-isometric linear system is uniquely determined by its transfer function whenever the state space is a Pontryagin space.
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Yang, A.M. A construction of unitary linear systems. Integr equ oper theory 19, 477–499 (1994). https://doi.org/10.1007/BF01299845
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DOI: https://doi.org/10.1007/BF01299845