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An Isaac Newton Institute Workshop

Quantum Graphs, their Spectra and Applications

Boundary Value Problems for Infinite Metric Graphs

Author: Robert Carlson (Univ. of Colorado, Colorado Springs)

Abstract

The second derivative operator with standard interior vertex conditions is considered on infinite metric graphs with finite volume or other smallness conditions. A large collection of self adjoint domains defined by local boundary conditions on the metric space completion of the graph is constructed for a rich family of metric graphs that are 'weakly connected'. The developed techniques also provide the solution of the Dirichlet problem for harmonic functions.