naa a22 4500 510783244 CHVBK 20180411083254.0 cr unu---uuuuu 180411e20130301xx s 000 0 eng 10.1007/s11856-012-0059-3 doi (NATIONALLICENCE)springer-10.1007/s11856-012-0059-3 On the spectral theory of trees with finite cone type [Elektronische Daten] [Matthias Keller, Daniel Lenz, Simone Warzel] 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 the 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. Hebrew University Magnes Press, 2012 Keller Matthias Mathematisches Institut, Friedrich Schiller Universität Jena, D-07745, Jena, Germany aut Lenz Daniel Mathematisches Institut, Friedrich Schiller Universität Jena, D-07745, Jena, Germany aut Warzel Simone Zentrum Mathematik, Technische Universität München, Boltzmannstraße 3, D-85747, Garching, Germany aut Israel Journal of Mathematics The Hebrew University Magnes Press 194/1(2013-03-01), 107-135 0021-2172 194:1<107 2013 194 11856 https://doi.org/10.1007/s11856-012-0059-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11856-012-0059-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Keller Matthias Mathematisches Institut, Friedrich Schiller Universität Jena, D-07745, Jena, Germany aut NATIONALLICENCE 700 1- Lenz Daniel Mathematisches Institut, Friedrich Schiller Universität Jena, D-07745, Jena, Germany aut NATIONALLICENCE 700 1- Warzel Simone Zentrum Mathematik, Technische Universität München, Boltzmannstraße 3, D-85747, Garching, Germany aut NATIONALLICENCE 773 0- Israel Journal of Mathematics The Hebrew University Magnes Press 194/1(2013-03-01), 107-135 0021-2172 194:1<107 2013 194 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer