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

Jens Bolte, Sebastian Egger, Ralf Rueckriemen

Research output: Contribution to journalArticlepeer-review

111 Downloads (Pure)


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
Issue number1
Early online date3 Dec 2014
Publication statusE-pub ahead of print - 3 Dec 2014

Cite this