Heat-kernel and Resolvent Asymptotics for Schrodinger Operators on Metric Graphs
Heat-kernel and Resolvent Asymptotics for Schrodinger Operators on Metric Graphs
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 …