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Constant J-unitary factor and operator-valued transfer functions

Pages: 48 - 56, Issue Special, July 2003

 Abstract        Full Text (192.2K)              

Yury ArlinskiÄ­ - Department of Mathematics, East Ukrainian National University, Lugansk, 91034, Ukraine (email)
Eduard TsekanovskiÄ­ - Department of Mathematics, POB 2044, Niagara University, NY 14109, United States (email)

Abstract: 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.

Keywords:  Keywords and Phrases
Mathematics Subject Classification:  Primary: 47A63, 47B25; Secondary: 47B65.

Received: September 2002; Published: April 2003.