Abstract
Explicit formulas for Wiener-Hopf factorization of rational matrix and analytic operator functions relative to a closed contour are constructed. The formulas are given in terms of a realization of the functions. Also formulas for the factorization indices are given.
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Bart, H., Gohberg, I., Kaashoek, M.A.: Minimal factorization of matrix and operator functions. Operator Theory: Advances and Applications, Vol.1. Basel-Boston-Stuttgart, Birkhäuser Verlag, 1979.
[] Bart, H. Gohberg, I., Kaashoek, M.A.: Wiener-Hopf factorization of analytic operator functions and realization. Rapport 231, Wiskundig Seminarium, Vrije Universiteit, Amsterdam, 1983.
[] Bart, H., Gohberg, I., Kaashoek, M.A.: Wiener-Hopf factorization and realization. In: Mathematical Theory of Networks and Systems, Proceedings of the MTNS-83 International Symposium, Beer Sheva, Israel, Lecture Notes in Control and Information Sciences, no. 58 (Ed. P. Fuhrmann), Springer Verlag, Berlin, 1984, pp.42–62.
[] Bart, H., Gohberg, I., Kaashoek, M.A.: Invariants for Wiener-Hopf equivalence of analytic operator functions. This volume.
[] Brodskii, M.S.: Triangular and Jordan representation of linear operators. Transl. Math. Monographs, Vol.32, Providence, R.I., Amer. Math. Soc., 1970.
[] Clancey, K., Gohberg, I.: Factorization of matrix functions and singular integral operators. Operator Theory: Advances and Applications, Vol.3, Basel-Boston-Stuttgart, Birkhäuser Verlag, 1981.
[] Gohberg, I.C., Feldman, I.A.: Convolution equations and project ion methods, for their solution. Transl. Math. Monographs, Vol.41, Providence, R.I., Amer. Math. Soc., 1974.
[] Gohberg, I.C., Krein, M.G.: Systems of integral equations on a half line with kernels depending on the difference of arguments. Amer. Math. Soc. Transl. (2) 14, 217–287 (1960).
[] Gohberg, I.C., Krein, M.G.: Theory and applications of Volterra operators in Hilbert space. Transl. Math. Monographs, Vol.24, Providence, R.I., Amer. Math. Soc., 1970.
[] Gohberg, I., Krupnik, N.: Einführung in die Theorie der eindimensionalen singulären Integraloperatoren. Basel-Boston-Stuttgart, Birkhäuser Verlag, 1979.
[] Gohberg, I., Kaashoek, M.A., Van Schagen, F.: Similarity of operator blocks and canonical forms. I General results, feedback equivalence and Kronecker indices. Integral Equations and Operator Theory 3, 350–396 (1980).
[] Gohberg, I.C., Leiterer, J.: A criterion for factorization of operator functions with respect to a contour. Sov. Math. Dokl. 14, No.2, 425–429 (1973).
[] Krein, M.G.: Integral equations on the half line with a kernel depending on the difference of the arguments. Amer. Math. Soc. Transl. (2) 22, 163–288 (1962).
[] Kaiman, R.E., Falb, P.F., Arbib, Μ.Α.: Topics in mathematical systems theory. New York, McGraw-Hill, 1969.
[] Kaashoek, M.A., Ran, A.C.M.: Symmetric Wiener-Hopf factorization of selfadjoint rational matrix functions and realization. This volume.
[] Wonham, W.H.: Linear Multivariable Control. Berlin, Springer Verlag, 1974.
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© 1986 Birkhäuser Verlag Basel
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Bart, H., Gohberg, I., Kaashoek, M.A. (1986). Explicit Wiener-Hopf Factorization and Realization. In: Gohberg, I., Kaashoek, M.A. (eds) Constructive Methods of Wiener-Hopf Factorization. OT 21: Operator Theory: Advances and Applications, vol 21. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7418-2_8
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DOI: https://doi.org/10.1007/978-3-0348-7418-2_8
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