Spectral analysis of complete graph with infinite chains

  • V.O. Lebid Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereschenkivska str., 01601, Kyiv, Ukraine
Keywords: infinite graph, matrix Jacobi, absolutely continuous spectrum, spectral decomposition, spectral density
Published online: 2014-07-14

Abstract


In the paper the detailed spectral analysis of a complete graph with semibounded infinite chains is given. The spectrum of a self-adjoint operator which is generated by the adjacency matrix of the graph is defined, the spectral measure is constructed, eigenvectors and spectral expansion in eigenvectors are provided.
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