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Paper detail

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

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.

preprint2014arXivOpen access
Jens BolteSebastian EggerRalf Rueckriemen
math-phmath.MPmath.SP
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Jens BolteSebastian EggerRalf Rueckriemen

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