Abstract
This chapter presents an introduction to the theory of unitary systems and their transfer functions. We already met transfer functions of the form I + C(λ − A)-1 B in earlier chapters. Here we are concerned with the case when the system matrix is a unitary operator acting on an infinite dimensional Hilbert space. Characteristic operator functions are transfer functions of such systems. In mathematical system theory often the starting point is the input-output map or the associated transfer function. In the theory of characteristic operator functions the situation is different. Here the main operator A, which is a contraction, comes first and the characteristic operator function serves as a unitary invariant for A.KeywordsTransfer FunctionUnitary OperatorInvariant SubspaceUnitary SystemLinear ManifoldThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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