D. Z. Arov, N. A. Rozhenko, “On the Relation between the Darlington Realizations of Matrix Functions from the Carathéodory Class and Their <nobr>$J_{p,r}$</nobr>-Inner SI-Dilations”, Mat. Zametki, 2011, Volume 90, Issue 6,Pages <nobr>821

On the Relation between the Darlington Realizations of Matrix Functions from the Carathéodory Class and Their $J_{p,r}$-Inner SI-Dilations

D. Z. Arov^a, N. A. Rozhenko^b

^a South Ukrainian State K. D. Ushynsky Pedagogical University
^b I. I. Mechnikov Odessa National University

Abstract: The paper is devoted to establishing a two-sided relation between the Darlington realizations of matrix functions from the Carathéodory class $\mathscr C^{p\times p}\Pi$ and their $J_{p,r}$-inner SI-dilations.

Keywords: Darlington realization of matrix functions, Carathéodory class of functions, SI (scattering-impedance)-dilation, meromorphic function, Smirnov class of functions.

UDC: 517

Received: 11.07.2009
Revised: 05.04.2010

DOI: 10.4213/mzm8537