Letters in Mathematical Physics

, Volume 104, Issue 9, pp 1079–1094 | Cite as

Approximations of Quantum-Graph Vertex Couplings by Singularly Scaled Rank-One Operators

  • Pavel Exner
  • Stepan S. Manko


We investigate approximations of the vertex coupling on a star-shaped graph by families of operators with singularly scaled rank-one interactions. We find a family of vertex couplings, generalizing the δ′-interaction on the line, and show that with a suitable choice of the parameters they can be approximated in this way in the norm-resolvent sense. We also analyze spectral properties of the involved operators and demonstrate the convergence of the corresponding on-shell scattering matrices.

Mathematics Subject Classification (2010)

81Q35 81Q10 


quantum graph vertex coupling approximation 


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Doppler Institute for Mathematical Physics and Applied MathematicsCzech Technical University in PraguePragueCzechia
  2. 2.Nuclear Physics Institute ASCRŘež near PragueCzechia
  3. 3.Department of Physics, Faculty of Nuclear Science and Physical EngineeringCzech Technical University in PragueDěčínCzechia

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