Stable Dissipative Linear Stationary Dynamical Scattering Systems
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In the theory of passive linear electrical networks, the Darlington method is well known as a realization of a finite ideal passive 1-port with losses via a finite ideal passive lossless 2-port closed by one resistance . The reflection coefficient Θ of such a 1-port is an element of the scattering matrix \(\tilde \Theta\) of a corresponding loss-less 2-port; the lossless behavior is indicated in the property that \(\tilde \Theta\) has unitary values on the boundary of the physical domain (in the right or upper half-plane, or inside the unit disk). The consideration of scattering matrices allowed Belevich to generalize Darlington’s result on finite ideal n-ports with losses . Darlington himself did not consider Θ and \(\tilde \Theta\) but other frequency characteristics: the impedance Zof 1-ports and the transmission matrix Ã of 2-ports (Z and Ã have simple representations by means of Θ and \(\tilde \Theta\)). In this way, the Darlington result was generalized to finite ideal n-ports with losses by V.P. Potapov  and his student E.Ya. Melamud .
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- D. Alpay, A. Dijksma, J. Rovnyak, and H.S.V. de SnooSchur functions operator colligations and reproducing kernel Pontryagin spacesOper. Theory Adv. Appl., vol. 96, Birkhäuser Verlag, Basel, 1997.Google Scholar
- D.Z. ArovUnitary couplings with losses (a theory of scattering with losses)Funkcional. Anal. i Prilozen. 8 (1974), no. 4, 5–22, English transi.:Funct. Anal. Appl.8(4): 280–294, 1974.Google Scholar
- D.Z. Arov, Asurvey on passive networks and scattering systems which are lossless or have minimal lossesAEU Archiv für Elektronik and Übertragungstechnik. International Journal of Electronics and Communication 49 (1995), no. 5/6, 252–265.Google Scholar
- D.Z. ArovPassive linear systems and scattering theoryDynamical systems, control, coding, computer vision (Padova, 1998), Birkhäuser, Basel, 1999, pp. 27–44.Google Scholar
- D.Z. Arov and M.A. Nudel’manThe conditions of similarity of all minimal passive realizations of a given transfer function (scattering or resistence)submitted.1999Google Scholar
- M.G. Krein and H. LangerOber die verallgemeinerten Resolventen und die charakteristische Funktion eines isometrischen Operators im Raume HHilbert space operators and operator algebras (Proc. Internat. Conf., Tihany, 1970), North-Holland, Amsterdam, 1972, pp. 353–399. Colloq. Math. Soc. János Bolyai, 5.Google Scholar
- M.G. Krein and Ju.L. Smul’janFractional linear transformations with operator coefficientsMat. Issled 2 (1967), no. 3, 64–96, English transl.: Amer.Math. Soc. Transl.(2), vol. 103, pages 125–152, 1974.Google Scholar
- Oleg NitzGeneralized resolvents of isometric linear relations in Pontryagin spaces. I. FoundationsOperator theory and related topics, Vol. II (Odessa, 1997), Birkhäuser, Basel, 2000, pp. 303–319.Google Scholar
- D.R. PikBlock lower triangular operators and optimal contractive systemsPh.D. thesis, Free University of Amsterdam, 1999.Google Scholar
- M. Rosenblum and J. RovnyakHardy classes and operator theoryOxford University Press, New York, 1985, Dover republication, New York, 1997.Google Scholar
- S.M. SaprikinThe theory of linear stationary passive scattering systems with Pontryagin state spacesDokl. Ukrainian Akad. Nauk, submitted.Google Scholar