Geodesic
Adjoint and self-adjoint differential operators on graphs
Electronic Journal of Differential Equations, Tome 1998 (1998).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 34B10, 47E05
Keywords: graph, differential operator, adjoint, self-adjoint extension 
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     author = {Carlson, Robert},
     title = {Adjoint and self-adjoint differential operators on graphs},
     journal = {Electronic Journal of Differential Equations},
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     volume = {1998},
     year = {1998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1998__1998__a2/}
}
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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/