Spectral determinant of Schrödinger operators on graphs. (English) Zbl 0958.58026
Summary: We study the spectral properties of the operator \((-\Delta+ V(x))\) on a graph. \((\Delta\) is the Laplacian and \(V(x)\) is some potential defined on the graph). In particular, we derive an expression for the spectral determinant that generalizes one previously obtained for the Laplacian operator.
MSC:
| 58J50 | Spectral problems; spectral geometry; scattering theory on manifolds |
| 58J52 | Determinants and determinant bundles, analytic torsion |
| 05C50 | Graphs and linear algebra (matrices, eigenvalues, etc.) |
