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

Jens Bolte, Sebastian Egger, Ralf Rueckriemen

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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 languageEnglish
Pages (from-to)129-165
Number of pages37
JournalApplied Mathematics Research Express
Volume2015
Issue number1
Early online date3 Dec 2014
DOIs
Publication statusE-pub ahead of print - 3 Dec 2014

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