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Matthias Keller

  1. Generalized solutions and spectrum for Dirichlet forms on graphs.

    Fri, 02/05/2010 - 16:01 — SomNambul
    Authors: Matthias Keller, Sebastian Haeseler
    Subjects: Spectral Theory
    Abstract

    We study the connection of the existence of solutions with certain properties
    and the spectrum of operators in the framework of regular Dirichlet forms on
    infinite graphs.

  2. On the spectral theory of trees with finite forward cone type.

    Thu, 01/21/2010 - 16:01 — SomNambul
    Authors: Daniel Lenz, Simone Warzel, Matthias Keller
    Subjects: Spectral Theory
    Abstract

    We study basic spectral features of graph Laplacians associated to 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.

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