Geodesic
Adjoint and self-adjoint differential operators on graphs
Electronic journal of differential equations, Tome 1998 (1998)
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.
Classification : 34B10, 47E05
Keywords: graph, differential operator, adjoint, self-adjoint extension 
@article{EJDE_1998__1998__a2,
     author = {Carlson,  Robert},
     title = {Adjoint and self-adjoint differential operators on graphs},
     journal = {Electronic journal of differential equations},
     year = {1998},
     volume = {1998},
     zbl = {0888.34055},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1998__1998__a2/}
}
TY  - JOUR
AU  - Carlson,  Robert
TI  - Adjoint and self-adjoint differential operators on graphs
JO  - Electronic journal of differential equations
PY  - 1998
VL  - 1998
UR  - http://geodesic.mathdoc.fr/item/EJDE_1998__1998__a2/
LA  - en
ID  - EJDE_1998__1998__a2
ER  - 
%0 Journal Article
%A Carlson,  Robert
%T Adjoint and self-adjoint differential operators on graphs
%J Electronic journal of differential equations
%D 1998
%V 1998
%U http://geodesic.mathdoc.fr/item/EJDE_1998__1998__a2/
%G en
%F EJDE_1998__1998__a2
Carlson,  Robert. Adjoint and self-adjoint differential operators on graphs. Electronic journal of differential equations, Tome 1998 (1998). http://geodesic.mathdoc.fr/item/EJDE_1998__1998__a2/