On the spectral theory of trees with finite cone type

Details On the spectral theory of trees with finite cone type On the spectral theory of trees with finite cone type

2010-01-20

arxiv.org/abs/1001.3600v2

Mathematics

Spectral Theory

18 pages, 1 figure

Scientific paper

We study basic spectral features of graph Laplacians associated with a class of rooted trees which contains all regular trees. Trees in this class can be generated by substitution processes. Their spectra are shown to be purely absolutely continuous and to consist of finitely many bands. The main result gives stability of absolutely continuous spectrum under sufficiently small radially label symmetric perturbations for non regular trees in this class. In sharp contrast, the absolutely continuous spectrum can be completely destroyed by arbitrary small radially label symmetric perturbations for regular trees in this class.

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