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New aspects of Krein's extension theory

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Abstract

The extension problem for closed symmetric operators with a gap is studied. A new kind of parametrization of extensions (the so-called Krein model) is developed. The notion of a singular operator plays the key role in our approach. We give an explicit description of extensions and establish the spectral properties of extended operators.

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Authors and Affiliations

  1. J. W. Goethe University, Frankfurt, Germany

    J. F. Brasche

  2. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    V. Koshmanenko

  3. Technical University, Berlin, Germany

    H. Neidhardt

Authors
  1. J. F. Brasche
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  2. V. Koshmanenko
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  3. H. Neidhardt
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Additional information

Published in Ukrainskii Matematicheskii Zhurnal, Vol. 46, Nos. 1–2, pp. 37–54, January–February, 1994.

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Brasche, J.F., Koshmanenko, V. & Neidhardt, H. New aspects of Krein's extension theory. Ukr Math J 46, 34–53 (1994). https://doi.org/10.1007/BF01056999

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  • DOI: https://doi.org/10.1007/BF01056999

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