most citedExotic eigenvalues and analytic resolvent for a graph with a shrinking edge

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math.SP2026

Two escape rates for negative eigenvalues of quantum graphs with a shrinking core

Gregory Berkolaiko, Denis Borisov, Marshall King +1

We study the negative spectrum of the Laplacian on a metric graph with general vertex matching conditions and with two length scales: a compact core whose edges have length of orde…

math.SP2023★ 1 cited

Exotic eigenvalues and analytic resolvent for a graph with a shrinking edge

Gregory Berkolaiko, Denis I. Borisov, Marshall King

We consider a metric graph consisting of two edges, one of which has length which we send to zero. On this graph we study the resolvent and spectrum of the Laplacian…