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Spectral analysis of metric graphs with infinite rays

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Abstract

We conduct a detailed analysis for finite metric graphs that have a semi-infinite chain (a ray) attached to each vertex. We show that the adjacency matrix of such a graph gives rise to a selfadjoint operator that is unitary equivalent to a direct sum of a finite number of simplest Jacobi matrices. This permitted to describe spectrums of such operators and to explicitly construct an eigenvector decomposition.

Key words: Metric graphs, adjacency matrix, Jacobi matrix, spectral analysis


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Article Information

TitleSpectral analysis of metric graphs with infinite rays
SourceMethods Funct. Anal. Topology, Vol. 20 (2014), no. 4, 391-396
MathSciNet MR3309675
zbMATH 1324.05118
MilestonesReceived 05/06/2014
CopyrightThe Author(s) 2014 (CC BY-SA)

Authors Information

L. P. Nizhnik
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine 


Citation Example

L. P. Nizhnik, Spectral analysis of metric graphs with infinite rays, Methods Funct. Anal. Topology 20 (2014), no. 4, 391-396.


BibTex

@article {MFAT751,
    AUTHOR = {Nizhnik, L. P.},
     TITLE = {Spectral analysis of metric graphs with infinite rays},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {20},
      YEAR = {2014},
    NUMBER = {4},
     PAGES = {391-396},
      ISSN = {1029-3531},
  MRNUMBER = {MR3309675},
 ZBLNUMBER = {1324.05118},
       URL = {http://mfat.imath.kiev.ua/article/?id=751},
}


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