Heat-kernel and resolvent asymptotics for Schroedinger operators on metric graphs
Autor: | Bolte, Jens, Egger, Sebastian, Rueckriemen, Ralf |
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Rok vydání: | 2014 |
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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 |
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