Adjoint and self-adjoint differential operators on graphs
Electron. J. Differ. Equ. 1998, Paper 6, 10 p. (1998)
Summary: A differential operator on a directed graph with weighted edges is characterized as a system of ordinary differential operators. A class of local operators is introduced to clarify which operators should be considered as defined on the graph. When the edge lengths have a positive lower bound, all local self-adjoint extensions of the minimal symmetric operator may be classified by boundary conditions at the vertices.
Mathematics Subject Classification
graph, differential operator, adjoint, self-adjoint extension