\({\mathcal{PT}}\) -Symmetric Waveguides and the Lack of Variational Techniques

  • David Krejčiřík
Open Problems


On a model of waveguide with non-Hermitian Robin-type boundary conditions, we demonstrate the need for a robust method establishing the existence of isolated eigenvalues for non-self-adjoint operators possessing both essential and discrete spectrum.

Mathematics Subject Classification (2010)

35P15 35J05 47B44 81Q12 


Robin Laplacian non-self-adjoint boundary conditions complex symmetric operator \({\mathcal{PT}}\) -symmetry waveguides discrete and essential spectra 


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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Department of Theoretical Physics, Nuclear Physics InstituteAcademy of SciencesŘežCzech Republic

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