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Multiplication by Diagonals and Reduction to Canonical Factorization

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Constructive Methods of Wiener-Hopf Factorization

Part of the book series: OT 21: Operator Theory: Advances and Applications ((OT,volume 21))

Abstract

The calculus of matrix functions in realized form is developed further. Special attention is paid to the operation of multiplications by diagonal matrix functions. The analysis yields a reduction of matrix functions to functions that admit canonical factorization.

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References

  1. 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.

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  2. Bart, H., Gohberg, I., Kaashoek, M.A.: Wiener-Hopf factorization of analytic operator functions and realization. Rapport 231, Wiskundig Seminarium, Vrije Universiteit, Amsterdam, 1983.

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  3. Bart, H., Gohberg, I., Kaashoek, M.A.: Explicit Wiener-Hopf factorization and realization. This volume.

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  4. Bart, H., Gohberg, I., Kaashoek, M.A.: Invariants for Wiener-Hopf equivalence of analytic operator functions. This volume.

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  5. Birkhoff, G.D.: A theorem on matrices of analytic functions. Math. Ann. 74, 122–133 (1913).

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  6. Chibotaru, I.S.: The reduction of systems of Wiener-Hopf equations to systems with vanishing indices. Bull. Akad. Stiince RSS Moldoven 8, 54–66 (1967) [Russian].

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  7. 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.

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Author information

Authors and Affiliations

  1. Econometrisch Instituut, Erasmus Universiteit, Postbus 1738, 3000 DR, Rotterdam, The Netherlands

    H. Bart

  2. Dept of Mathematical Sciences The Raymond and Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, Ramat-Avid, Israel

    I. Gohberg

  3. Subfaculteit Wiskunde en InformaticaVrije Universiteit, Postbus 7161, 1007 MC, Amsterdam, The Netherlands

    M. A. Kaashoek

Authors
  1. H. Bart
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  2. I. Gohberg
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  3. M. A. Kaashoek
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Editor information

I. Gohberg M. A. Kaashoek

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© 1986 Birkhäuser Verlag Basel

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Bart, H., Gohberg, I., Kaashoek, M.A. (1986). Multiplication by Diagonals and Reduction to Canonical Factorization. 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_10

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  • DOI: https://doi.org/10.1007/978-3-0348-7418-2_10

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-7420-5

  • Online ISBN: 978-3-0348-7418-2

  • eBook Packages: Springer Book Archive

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