| Abstract: |
| The Evans function is a well known tool for locating spectra of differential operators in one spatial dimension. We construct a multidimensional analogue as the modified Fredholm determinant of a ratio of Dirichlet-to-Robin operators on the boundary. This gives a tool for studying the eigenvalue counting functions of second-order elliptic operators that need not be self-adjoint. In the self-adjoint case we relate our construction to the Maslov index, another well known tool in the spectral theory of differential operators. |
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