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An Overview of Matrix Factorization Theory and Operator Applications

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Factorization and Integrable Systems

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 141))

Abstract

These lecture notes present an extensive review of the factorization theory of matrix functions relative to a curve with emphasis on the developments of the last 20–25 years. The classes of functions considered range from rational and continuous matrix functions to matrix functions with almost periodic or even semi almost periodic entries. Also included are recent results about explicit factorization based on the state space method from systems theory, with examples from linear transport theory. Related applications to Riemann-Hilbert boundary value problems and the Fredholm theory of various classes of singular integral operators are described too. The applications also concern inversion of singular integral operators of different types, including Wiener-Hopf and Toeplitz operators.

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Authors and Affiliations

  1. School of Mathematics, Tel-Aviv Universtity, Ramat-Aviv, Tel-Aviv, 69978, Israel

    I. Gohberg

  2. Department of Mathematics, Vrije Universiteit, De Boelelaan 1081a, 1081 HV, Amsterdam, The Netherlands

    M. A. Kaashoek

  3. Department of Mathematics, College of William and Mary, P.O. Box 8795, Williamsburg, VA, 23187-8795, USA

    I. M. Spitkovsky

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  1. I. Gohberg
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  2. M. A. Kaashoek
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  3. I. M. Spitkovsky
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Editors and Affiliations

  1. School of Mathematical Sciences, Tel Aviv University, IL - Ramat Aviv, 69978, Israel

    Israel Gohberg

  2. Raymond and Beverly Sackler, Tel Aviv University, IL - Ramat Aviv, 69978, Israel

    Israel Gohberg

  3. Faculty of Exact Sciences, Tel Aviv University, IL - Ramat Aviv, 69978, Israel

    Israel Gohberg

  4. A.D. Matematica, FCT, Universidade do Algarve Campus de Gambelas, 8000-117, Faro, Portugal

    Nenad Manojlovic

  5. Departamento de Matemática Instituto Superior Técnico, Ave. Rovisco Pais, 1049-001, Lisboa, Portugal

    António Ferreira dos Santos

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Gohberg, I., Kaashoek, M.A., Spitkovsky, I.M. (2003). An Overview of Matrix Factorization Theory and Operator Applications. In: Gohberg, I., Manojlovic, N., dos Santos, A.F. (eds) Factorization and Integrable Systems. Operator Theory: Advances and Applications, vol 141. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8003-9_1

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  • DOI: https://doi.org/10.1007/978-3-0348-8003-9_1

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9400-5

  • Online ISBN: 978-3-0348-8003-9

  • eBook Packages: Springer Book Archive

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