Spectral analysis of complete graph with infinite chains

V.O. Lebid

doi:10.15330/cmp.6.1.73-78

Spectral analysis of complete graph with infinite chains

Authors

V.O. Lebid Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereschenkivska str., 01601, Kyiv, Ukraine

https://doi.org/10.15330/cmp.6.1.73-78

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.