Electronic Journal of Differential Equations,
Vol. 1998(1998), No. 06, pp. 1-10.

Title: Adjoint and self-adjoint differential operators on graphs  

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

Abstract:
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.


 
Submitted August 24, 1997. Published February 26, 1998.
Math Subject Classification: 34B10, 47E05. 
Key Words: Graph; differential operator; adjoint; self-adjoint extension.