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Solution of the Truncated Matrix Hamburger Moment Problem According to M.G. Krein

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Operator Theory and Related Topics

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 118))

Abstract

The matrix version of the truncated Hamburger moment problem is considered. The criterium of its solvability is specified and a matrix version of the scalar Nevanlinna formula describing all possible solutions is established. As a main tool methods of the theory of extensions of symmetric operators and, in particular, the M.G. Krein formula for generalized resolvents are used.

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This author was supported by the Government of Ukraine and the USA Civillian Research and Development Foundation, Award UM1 — 298.

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Author information

Authors and Affiliations

  1. Department of Theoretical Physics, University of Odessa, 270026, Odessa, Ukraine

    V. M. Adamyan

  2. Department of Applied Mathematics, Polytechnic University of Valencia, E-46071, Valencia, Spain

    I. M. Tkachenko

Authors
  1. V. M. Adamyan
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  2. I. M. Tkachenko
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Editor information

Editors and Affiliations

  1. Department of Theoretical Physics, University of Odessa, 270026, Odessa, Ukraine

    V. M. Adamyan

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

    I. Gohberg

  3. Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    M. Gorbachuk  & V. Gorbachuk  & 

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

    M. A. Kaashoek

  5. Department of Mathematics, Technical University of Vienna, Wiedner Hauptstrasse 8-10/1411, 1040, Vienna, Austria

    H. Langer

  6. Institute of Mathematics, Economics and Mechanics, Odessa State University, 270057, Dvoryanskaya str. 2, Odessa, Ukraine

    G. Popov

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© 2000 Springer Basel AG

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Adamyan, V.M., Tkachenko, I.M. (2000). Solution of the Truncated Matrix Hamburger Moment Problem According to M.G. Krein. In: Adamyan, V.M., et al. Operator Theory and Related Topics. Operator Theory: Advances and Applications, vol 118. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8413-6_3

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  • DOI: https://doi.org/10.1007/978-3-0348-8413-6_3

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9557-6

  • Online ISBN: 978-3-0348-8413-6

  • eBook Packages: Springer Book Archive

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