Abstract
In this chapter we consider special types of L-systems and study the properties of their transfer functions. In the first two sections we will use the notion of an auxiliary canonical system to prove a theorem about the constant J-unitary factor. The theorem states that if an operator-valued function W(z) belongs to the class Ω0(R,J) described in Section 7.2, then for an arbitrary J-unitary operator B the functions W(z)B and BW(z) again belong to the same class Ω0(R, J). Consequently, they can be realized as transfer functions of the same type of Lsystem. We will construct this new realizing system and show that it contains the same unbounded operator T but different channel operators K.
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