Olaf Post am 1.6.

Titel:
Approximations of 1-dimensional structures

Abstract

A 1-dimensional branched structure can be considered as a metric graph,
i.e.,
a graph where each edge has a length. Such structures are models for
networks
or nano-structures. We consider higher-dimensional sets approaching the
1-dimensional structure together with the Laplace operator on it. The
higher-dimensional approach can often be used to identify the "natural"
candidates of operators on the graph. In this talk we will show that the
spectra converge as well as functions of the operators like the resolvent or
the time evolution. The technical heart of the proof is a criterion assuring
the spectral convergence under assumptions on the quadratic form of the
approaching and limit operator, respectively.