Download The state space method: generalizations and applications by Daniel Alpay, Israel Gohberg PDF

By Daniel Alpay, Israel Gohberg

"The kingdom house strategy constructed within the final many years permits us to check the idea of linear platforms by utilizing instruments from the speculation of linear operators; conversely, it had a powerful effect on operator thought introducing new questions and themes. "The current quantity encompasses a number of essays representing a few of the fresh advances within the kingdom area process. equipment lined contain noncommutative platforms idea, new facets of the speculation of discrete platforms, discrete analogs of canonical structures, and new purposes to the idea of Bezoutiants and convolution equations. The articles within the quantity should be of curiosity to natural and utilized mathematicians, electric engineers and theoretical physicists.

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2 Minimal realizations in non-commutative de Branges–Rovnyak spaces . . . . . . . . . . . . . . . . . . . 3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 Matrix-J-unitary Rational Formal Power Series 51 1. Introduction In the present paper we study a non-commutative analogue of rational matrixvalued functions which are J-unitary on the imaginary line or on the unit circle and, as a special case, J-inner ones.

PhD thesis, The Weizmann Institute of Sciences, 1986. G. Kre˘n. ˘ Continuous analogues of propositions for polynomials orthogonal on the unit circle. Dokl. Akad. Nauk. SSSR, 105:637–640, 1955. G. Kre˘n. Topics in differential and integral equations and operator theory, volume 7 of Operator theory: Advances and Applications. Birkhauser ¨ Verlag, Basel, 1983. Edited by I. Gohberg, Translated from the Russian by A. Iacob. G. Kre˘n ˘ and H. Langer. Uber die verallgemeinerten Resolventen und die charakteristische Funktion eines isometrischen Operators im Raume Πk .

1 Minimal Givone–Roesser realizations and the Stein equation . . . 2 The associated structured Hermitian matrix . . . . . . . . . . . 3 Minimal matrix-J-unitary factorizations . . . . . . . . . . . . . 4 Matrix-unitary rational formal power series . . . . . . . . . . . . 85 6 Matrix-J-inner rational formal power series . . . . . . . . . . . . . . 1 A multivariable non-commutative analogue of the half-plane case . . . . . . . .

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