Heat-kernel and resolvent asymptotics for Schroedinger operators on metric graphs
Mathematical Physics
2014-10-31 v2 math.MP
Spectral Theory
Abstract
We consider Schroedinger operators on compact and non-compact (finite) metric graphs. For such operators we analyse their spectra, prove that their resolvents can be represented as integral operators and introduce trace-class regularisations of the resolvents. Our main result is a complete asymptotic expansion of the trace of the (regularised) heat-semigroup generated by the Schroedinger operator. We also determine the leading coefficients in the expansion explicitly.
Cite
@article{arxiv.1406.1045,
title = {Heat-kernel and resolvent asymptotics for Schroedinger operators on metric graphs},
author = {Jens Bolte and Sebastian Egger and Ralf Rueckriemen},
journal= {arXiv preprint arXiv:1406.1045},
year = {2014}
}
Comments
This article has been accepted for publication in Applied Mathematics Research Express Published by Oxford University Press