A simplicity criterion for symmetric operator on a graph. (English) Zbl 1313.47093

Ashurova, E. N.; Kandagura, A. N.; Karpenko, I. I.

Methods Funct. Anal. Topol. 20, No. 2, 117-123 (2014).

The authors consider a minimal symmetric operator on a finite metric graph corresponding to the differential expression \(-\frac{d^2}{dx^2}\) on edges of the graph. They compute the deficiency indices and give necessary and sufficient conditions, in terms of the geometry of a graph, for the operator to be simple.

Reviewer: Anatoly N. Kochubei (Kyïv)

MSC:

47E05	General theory of ordinary differential operators
34B45	Boundary value problems on graphs and networks for ordinary differential equations
39B12	Iteration theory, iterative and composite equations

Keywords:

differential operator on a graph; deficiency index; simple symmetric operator