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Krein Systems

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Modern Analysis and Applications

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 191))

Abstract

In the present paper we extend results of M.G. Krein associated to the spectral problem for Krein systems to systems with matrix-valued accelerants with a possible jump discontinuity at the origin. Explicit formulas for the accelerant are given in terms of the matrizant of the system in question. Recent developments in the theory of continuous analogs of the resultant operator play an essential role.

Daniel Alpay wishes to thank the Earl Katz family for endowing the chair which supported his research. The work of Alexander Sakhnovich was supported by the Austrian Science Fund (FWF) under Grant no. Y330.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Ben-Gurion University of the Negev, 84105, Beer-Sheva, Israel

    D. Alpay

  2. School of Mathematical Sciences, The Raymond and Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, 69989, Tel-Aviv, Ramat-Aviv, Israel

    I. Gohberg

  3. Afdeling Wiskunde, Faculteit der Exacte Wetenschappen Vrije Universiteit, De Boelelaan 1081a, 1081, HV Amsterdam, The Netherlands

    M. A. Kaashoek

  4. Department of Mathematics, Technion, Israel Institute of Technology, 32000, Haifa, Israel

    L. Lerer

  5. Fakultät für Mathematik, Universität Wien, 15 Nordbergstrasse, A-1090, Wien, Austria

    A. Sakhnovich

Authors
  1. D. Alpay
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  2. I. Gohberg
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  3. M. A. Kaashoek
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  4. L. Lerer
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  5. A. Sakhnovich
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Editor information

Editors and Affiliations

  1. Department of Theoretical Physics, Odessa National I.I. Mechnikov University, Dvoryanska st. 2, 65026, Odessa, Ukraine

    Vadim M. Adamyan

  2. Department of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, 69978, Ramat Aviv, Israel

    Israel Gohberg

  3. Insitute of Mathematics, Ukrainian National Academy of Sciences, Tereshchenkivska st., 01601, Kyiv-4, Ukraine

    Anatoly Kochubei , Yurij Berezansky , Myroslav Gorbachuk  & Valentyna Gorbachuk , ,  & 

  4. Department of Mathematical Physics, Odessa National I.I. Mechnikov University, Dvoryanska st. 2, 65026, Odessa, Ukraine

    Gennadiy Popov

  5. Institute of Analysis and Scientific Computing, Technical University of Vienna, Wiedner Hauptstrasse 8-10, 1040, Vienna, Austria

    Heinz Langer

Additional information

In memory of Mark Grigorievich Krein, with appreciation of his many great discoveries, on the occasion of his Centennial.

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© 2009 Birkhäuser Verlag Basel/Switzerland

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Alpay, D., Gohberg, I., Kaashoek, M.A., Lerer, L., Sakhnovich, A. (2009). Krein Systems. In: Adamyan, V.M., et al. Modern Analysis and Applications. Operator Theory: Advances and Applications, vol 191. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-9921-4_3

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