Heat-kernel and resolvent asymptotics for Schroedinger operators on metric graphs

Autor:	Bolte, Jens, Egger, Sebastian, Rueckriemen, Ralf
Rok vydání:	2014
Předmět:	Mathematical Physics Mathematics - Spectral Theory 81Q35 81Q10 58J50 47A10
Druh dokumentu:	Working Paper
Popis:	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. Comment: This article has been accepted for publication in Applied Mathematics Research Express Published by Oxford University Press
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1406.1045 Zobrazit plný text záznamu View this record from Arxiv