- 06-17 Vadim Kostrykin and Robert Schrader
- Laplacians on Metric Graphs: Eigenvalues, Resolvents and Semigroups
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Jan 20, 06
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Abstract. The main objective of the present work is to study the negative spectrum of
(differential) Laplace operators on metric graphs as well as their
resolvents and associated heat semigroups. We prove an upper bound on the
number of negative eigenvalues and a lower bound on the spectrum of Laplace
operators. Also we provide a sufficient condition for the associated heat
semigroup to be positivity preserving.
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