Singular Schrödinger operators and Robin billiards

Spectral properties and asymptotic expansions
  • Pavel Exner


This paper summarizes the contents of a plenary talk at the Pan African Congress of Mathematics held in Rabat in July 2017. We provide a survey of recent results on spectral properties of Schrödinger operators with singular interactions supported by manifolds of codimension one and of Robin billiards with the focus on the geometrically induced discrete spectrum and its asymptotic expansions in term of the model parameters.


Schrödinger operators Singular interactions Robin billiards Discrete spectrum Asymptotic expansions 

Mathematics Subject Classification

81Q37 35J10 



Our recent results discussed in this survey are the result of a common work with a number of colleagues, in the first place Jaroslav Dittrich, Sylwia Kondej, Christian Kühn, Vladimir Lotoreichik, Konstantin Pankrashkin, and Axel Pérez-Obiol whom I am grateful for the pleasure of collaboration. The research was supported by the Czech Science Foundation (GAČR) within the project 17-01706S. Thanks also go to the referee for careful reading of the manuscript.


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Copyright information

© African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Theoretical PhysicsNuclear Physics Institute, Czech Academy of SciencesŘež near PragueCzechia
  2. 2.Doppler Institute for Mathematical Physics and Applied MathematicsCzech Technical UniversityPragueCzechia

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