A note on the Gaffney Laplacian on infinite metric graphs. (English) Zbl 1475.35374
Summary: We show that the deficiency indices of the minimal Gaffney Laplacian on an infinite locally finite metric graph are equal to the number of finite volume graph ends. Moreover, we provide criteria, formulated in terms of finite volume graph ends, for the Gaffney Laplacian to be closed.
MSC:
| 35R02 | PDEs on graphs and networks (ramified or polygonal spaces) |
| 47B25 | Linear symmetric and selfadjoint operators (unbounded) |
| 81Q10 | Selfadjoint operator theory in quantum theory, including spectral analysis |
| 05C50 | Graphs and linear algebra (matrices, eigenvalues, etc.) |
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