Constant J-unitary factor and operator-valued transfer functions

Yury Arlinskiĭ; Eduard Tsekanovskiĭ

doi:10.3934/proc.2003.2003.48

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2003, Volume 2003: 48-56. Doi: 10.3934/proc.2003.2003.48 open access

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Constant J-unitary factor and operator-valued transfer functions

Yury Arlinskiĭ^1, and
Eduard Tsekanovskiĭ^2,

1.
Department of Mathematics, East Ukrainian National University, Lugansk, 91034
2.
Department of Mathematics, POB 2044, Niagara University, NY 14109

Received: August 31, 2002

Published: March 2003

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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.

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

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