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- Publisher
- Oxford University Press
- Copyright
- © The author(s) 2014. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: [email protected].
- ISSN
- 1687-1200
- eISSN
- 1687-1197
- DOI
- 10.1093/amrx/abu009
- Publisher site
- See Article on Publisher Site
Abstract
We consider Schrödinger operators on compact and noncompact (finite) metric graphs. For such operators we analyze their spectra, prove that their resolvents can be represented as integral operators, and introduce trace-class regularizations of the resolvents. Our main result is a complete asymptotic expansion of the trace of the (regularized) heat-semigroup generated by the Schrödinger operator. We also determine the leading coefficients in the expansion explicitly.
Journal
Applied Mathematics Research Express – Oxford University Press
Published: Dec 3, 2015