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Constant J-unitary factor and operator-valued transfer functions

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  • We study linear, conservative, stationary dynamical systems (l.c.s.d.s) with unbounded main operator and their transfer operator-valued functions. A new class of transfer operator-valued functions is introduced and shown that this class is invariant with respect to multiplication (from the left, from the right or both) by a constant J-unitary operator. The problem how to realize the product W(z)B as a transfer function of some l.c.s.d.s with an arbitrary J-unitary operator B and given realization of W(z) is considered.
    Mathematics Subject Classification: Primary: 47A63, 47B25; Secondary: 47B65.


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