Heat-kernel and Resolvent Asymptotics for Schrödinger Operators on Metric Graphs

Jens Bolte; Sebastian Egger; Ralf Rueckriemen

doi:10.1093/amrx/abu009

Heat-kernel and Resolvent Asymptotics for Schrödinger Operators on Metric Graphs

Jens Bolte
, Sebastian Egger
, Ralf Rueckriemen

Research output: Contribution to journal › Article › peer-review

171 Downloads (Pure)

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.

Original language	English
Pages (from-to)	129-165
Number of pages	37
Journal	Applied Mathematics Research Express
Volume	2015
Issue number	1
Early online date	3 Dec 2014
DOIs	https://doi.org/10.1093/amrx/abu009
Publication status	E-pub ahead of print - 3 Dec 2014

Access to Document

10.1093/amrx/abu009

Accepted ManuscriptAccepted author manuscript, 446 KB

http://arxiv.org/abs/1406.1045

Cite this

@article{31bd367d289a4f86947b4fd3f6040392,

title = "Heat-kernel and Resolvent Asymptotics for Schr{\"o}dinger Operators on Metric Graphs",

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.",

author = "Jens Bolte and Sebastian Egger and Ralf Rueckriemen",

year = "2014",

month = dec,

day = "3",

doi = "10.1093/amrx/abu009",

language = "English",

volume = "2015",

pages = "129--165",

journal = "Applied Mathematics Research Express",

issn = "1687-1200",

publisher = "Oxford University Press",

number = "1",

}

TY - JOUR

T1 - Heat-kernel and Resolvent Asymptotics for Schrödinger Operators on Metric Graphs

AU - Bolte, Jens

AU - Egger, Sebastian

AU - Rueckriemen, Ralf

PY - 2014/12/3

Y1 - 2014/12/3

N2 - 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.

AB - 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.

U2 - 10.1093/amrx/abu009

DO - 10.1093/amrx/abu009

M3 - Article

SN - 1687-1200

VL - 2015

SP - 129

EP - 165

JO - Applied Mathematics Research Express

JF - Applied Mathematics Research Express

IS - 1

ER -