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Ukrainian Mathematical Journal

, Volume 65, Issue 8, pp 1180–1202 | Cite as

Scattering Theory for 0-Perturbed \( \mathcal{P}\mathcal{T} \) -Symmetric Operators

  • A. I. Hrod
  • S. O. Kuzhel’
Article

The aim of the present work is to develop the scattering theory for 0-perturbed \( \mathcal{P}\mathcal{T} \) -symmetric operators by using the Lax–Phillips method. The presence of a stable \( \mathcal{C} \) -symmetry leading to the property of selfadjointness (with proper choice of the inner product) for these \( \mathcal{P}\mathcal{T} \) -symmetric operators is described in terms of the corresponding S -matrix (scattering matrix).

Keywords

Hilbert Space Bounded Linear Operator Symmetric Operator Conjugation Operator Weyl Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • A. I. Hrod
    • 1
  • S. O. Kuzhel’
    • 2
  1. 1.Institute of MathematicsUkrainian National Academy of SciencesKyivUkraine
  2. 2.AGH University Science and TechnologyKrakowPoland

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