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Singularities of Generalized Strings

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Operator Theory and Indefinite Inner Product Spaces

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 163))

Abstract

We investigate the structure of a maximal chain of matrix functions whose Weyl coefficient belongs to \( \mathcal{N}_\kappa ^ + \) . It is shown that its singularities must be of a very particular type. As an application we obtain detailed results on the structure of the singularities of a generalized string which are explicitly stated in terms of the mass function and the dipole function. The main tool is a transformation of matrices, the construction of which is based on the theory of symmetric and semibounded de Branges spaces of entire functions. As byproducts we obtain inverse spectral results for the classes of symmetric and essentially positive generalized Nevanlinna functions.

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Author information

Authors and Affiliations

  1. Institut für Analysis und Scientific Computing, Technische Universität Wien, Wiedner Hauptstr. 8-10/101, A-1040, Wien, Austria

    Michael Kaltenbäck & Harald Woracek

  2. Institute der Wiskunde en Informatica, Rijksuniversiteit Groningen, Postbus 800, 9700 AV, Groningen, The Netherlands

    Henrik Winkler

Authors
  1. Michael Kaltenbäck
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  2. Henrik Winkler
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  3. Harald Woracek
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Strathclyde, 26 Richmond Street, Glasgow, G1 1XH, UK

    Matthias Langer

  2. Institut für Analysis und Scientific Computing, Technische Universität Wien, Wiedner Hauptstrasse 8-10 / 101, 1040, Wien, Austria

    Annemarie Luger  & Harald Woracek  & 

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© 2005 Birkhäuser Verlag Basel/Switzerland

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Kaltenbäck, M., Winkler, H., Woracek, H. (2005). Singularities of Generalized Strings. In: Langer, M., Luger, A., Woracek, H. (eds) Operator Theory and Indefinite Inner Product Spaces. Operator Theory: Advances and Applications, vol 163. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7516-7_9

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