Realization and Linearization of Operator Functions

Part of the Operator Theory: Advances and Applications book series (OT, volume 178)


The main problem addressed in this chapter is the realization problem for operatorvalued functions. Given such a function the problem is to find a system for which the transfer function coincides with the given function. In the first section we consider rational operator functions, and in the second analytic ones. In Section 4.3 it is shown that, in a certain sense, the transfer function of a system with an invertible external operator can be reduced to a linear function, and we use this reduction to describe the singularities of the transfer function. In the final section a connection between Schur complements and linearization is described.


Banach Space Transfer Function Operator Function Riemann Sphere Complex Banach Space 
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© Birkhäuser Verlag AG 2008

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