Spectral analysis of complete graph with infinite chains

V. O. Lebid

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.

Keywords


infinite graph, matrix Jacobi, absolutely continuous spectrum, spectral decomposition, spectral density

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