Abstract
The concept of block-similarity introduced in part I and its extension to the infinite dimensional case developed here provide a unified approach to state feedback theory for systems, the theory of Kronecker indices and Wiener-Hopf factorization problems. In this part we concentrate on the connections with the factorization theory.
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References
Bart, H., Gohberg, I., Kaashoek, M.A.: Minimal factorization of matrix and operator functions. OT1. Basel, Birkhäuser Verlag, 1979.
Fuhrmann, P.A., Willems, J.C.: Factorization indices at infinity for rational matrix functions. Integral Equations and Operator Theory 2(3) (1979) 187–301.
Gohberg, I., Kaashoek, M.A., Lay, D.C.: Equivalence, linearization and decompositions of holomorphic operator functions. J. Funct. Anal. 28 (1978), 102–144.
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(3) (1980), 350–396.
Gohberg, I., Lerer, L.: Factorization indices and Kronecker indices of matrix polynomials. Integral Equations and Operator Theory 2(2) (1979), 199–243.
Gohberg, I., Lerer, L., Rodman, L.: Factorization indices for matrix polynomials. Bull. Amer. Math. Soc. 84(2) (1978) 275–277.
Gohberg, I., Lerer, L., Rodman, L.: Stable factorizations of operator polynomials and spectral divisions simply behaved at infinity. I and II. J. of Math. Analysis and Appl. 74 (1980), 401–431; 75 (1980), 1-40.
Gohberg, I., Leiterer, J.: General theorems on the factorization of operator-valued functions with respect to a contour. I. Holomorphic functions (Russian), Acta Sci. Math. (Szeged) 34 (1973), 103–120.
Kaashoek, M.A., van der Mee, C.V.M., Rodman, L.: Analytical equivalence of holomorphic operator functions and linearization. (In preparation).
Rowley, B.: Wiener-Hopf factorization of operator polynomials. Integral Equations and Operator Theory 3(3) (1980), 437–462.
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© 1981 Springer Basel AG
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Gohberg, I., Kaashoek, M.A., van Schagen, F. (1981). Similarity of Operator Blocks and Canonical Forms. II. Infinite Dimensional Case and Wiener-Hopf Factorization. In: Apostol, C., Douglas, R.G., Nagy, B.S., Voiculescu, D., Arsene, G. (eds) Topics in Modern Operator Theory. Operator Theory: Advances and Applications, vol 2. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5456-6_10
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DOI: https://doi.org/10.1007/978-3-0348-5456-6_10
Publisher Name: Birkhäuser, Basel
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Online ISBN: 978-3-0348-5456-6
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