Adjoint and self-adjoint differential operators on graphs

Robert Carlson

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.

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Robert Carlson University of Colorado at Colorado Springs Colorado Springs, CO 80933, USA e-mail: carlson@math.uccs.edu

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