Open Access

Spectral analysis of metric graphs with infinite rays


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

Full Text

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 

Google Scholar Metrics

Citing articles in Google Scholar
Similar articles in Google Scholar

Export article

Save to Mendeley

Citation Example

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


@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 = {},

All Issues