Spectral analysis of locally finite graphs with one infinite ray
DOI:
https://doi.org/10.15407/dopovidi2014.03.029Keywords:
finite graphs, infinite ray, spectral analysisAbstract
A complete spectral analysis of countable graphs defined as the union of a finite graph and a semibounded infinite chain is given. The spectrum of the adjacency matrix of graphs is defined, a spectral measure is constructed, the eigenvectors and the spectral expansion in eigenvectors are presented.
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Tsvetkovich D., Dub M., Zakhs Kh. Spectra of graphs. Theory and application. Kyiv: Nauk. dumka, 1984 (in Russian).
Moskaleva Yu. P., Samoilenko Yu. S. Introduction to the spectral theory of graphs. Kyiv: Tsentr ucheb. lit., 2007 (in Russian).
Brouwer A. E., Haemers W. H. Spectra of graphs. New York: Springer, 2012. https://doi.org/10.1007/978-1-4614-1939-6
Mohar B. Linear Algebra Appl., 1982, 48: 245–256. https://doi.org/10.1016/0024-3795(82)90111-2
Mohar B., Woess W. Bull. London Math. Soc., 1989, 21: 209–234. https://doi.org/10.1112/blms/21.3.209
Mantoiu M., Richard S., Tiedra de Aldecoa R. Spectral analysis for adjacency operators on graphs. arXiv:math-ph/0603020v1 7 Mar 2006.
von Below J. Linear Algebra Appl., 2009, 431: 1–19. https://doi.org/10.1016/j.laa.2008.10.030
Pokornyi Yu. V., Penkin O. M., Pryadiev V. L. et al. Differential equations on geometric graphs. Moscow: Fizmatlit, 2004 (in Russian).
Berezansky Yu. M. Expansion in eigenfunctions of self-adjoint operators. Kyiv: Nauk. dumka, 1965 (in Russian).
Simon B. Szego’s theorem and its descendants: Spectral theory for L2 perturbations of orthogonal polynomials. Princeton, NY: Princeton Univ. Press, 2011.
Lebid V. O., Nyzhnyk L. P. Nauk. zap. NaUKMA, 2013, 139: 18–22 (in Russian).
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