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-Symmetric Laplace Operators on Star Graphs: Real Spectrum and Self-Adjointness

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  • Maria Astudillo
  • Pavel Kurasov
  • Muhammad Usman

Abstract

How ideas of -symmetric quantum mechanics can be applied to quantum graphs is analyzed, in particular to the star graph. The class of rotationally symmetric vertex conditions is analyzed. It is shown that all such conditions can effectively be described by circulant matrices: real in the case of odd number of edges and complex having particular block structure in the even case. Spectral properties of the corresponding operators are discussed.

Suggested Citation

  • Maria Astudillo & Pavel Kurasov & Muhammad Usman, 2015. "-Symmetric Laplace Operators on Star Graphs: Real Spectrum and Self-Adjointness," Advances in Mathematical Physics, Hindawi, vol. 2015, pages 1-9, December.
    • Handle: RePEc:hin:jnlamp:649795
    DOI: 10.1155/2015/649795
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