Peter Stollmann
Delone measures of finite local complexity and applications to spectral theory of one-dimensional continuum models of quasicrystals.
Sat, 03/20/2010 - 16:01 — SomNambulAuthors: Daniel Lenz, Peter Stollmann, Steffen Klassert
Subjects: Mathematical Physics
AbstractWe study measures on the real line and present various versions of what it
means for such a measure to take only finitely many values. We then study
perturbations of the Laplacian by such measures. Using Kotani-Remling theory,
we show that the resulting operators have empty absolutely continuous spectrum
if the measures are not periodic. When combined with Gordon type arguments this
allows us to prove purely singular continuous spectrum for some continuum
models of quasicrystals.Percolation Hamiltonians.
Mon, 03/01/2010 - 16:01 — SomNambulAuthors: Peter Stollmann, Peter Müller
Subjects: Mathematical Physics
AbstractThere has been quite some activity and progress concerning spectral
asymptotics of random operators that are defined on percolation subgraphs of
different types of graphs. In this short survey we record some of these results
and explain the necessary background coming from different areas in
mathematics: graph theory, group theory, probability theory and random
operators.Generalized eigenfunctions and spectral theory for strongly local Dirichlet forms.
Tue, 09/08/2009 - 12:16 — SomNambulAuthors: Daniel Lenz, Peter Stollmann, Ivan Veselic
Subjects: Spectral Theory
AbstractWe present an introduction to the framework of strongly local Dirichlet forms
and discuss connections between the existence of certain generalized
eigenfunctions and spectral properties within this framework. The range of
applications is illustrated by a list of examples.
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